The warm spell will follow a chilly night for parts of the UK, with an overnight frost affecting parts of northern England, Wales, the Midlands and South West.
Forecaster Marco Petagna said: "We're looking tomorrow (Monday) at around 16C (61F), with about a 30% chance of getting to 17 or 18C (62-64F) somewhere in the South or South East.
"Even that's just a little bit shy of this year's record, but certainly warm."
Temperatures will have to soar higher than the 18.3C (65F) recorded on February 20 in Northolt, north-west London, and Kew Gardens, south-west London to become the hottest day of 2017.
While it will be dry and reasonably sunny in the South and South East of the country, towards the North and North West there will be more cloud and the chance of drizzle for the first half of the week.
On Tuesday there could be gales in North and north-west Scotland, with gusts of up to 60 mph.
Towards the end of the week temperatures will fall but remain just above the average maximum highs for mid March - 8 or 9C (46-48F) in the North and between 9 and 11C (48-52F) in the South.
But Mr Petagna quashed hopes that it could be the hottest March week ever, as thousands of race-goers prepare to descend on Cheltenham.
The forecaster said it was unlikely that the mercury will reach 25.6C (78F) - the highest ever March temperature recorded on March 29 in 1968 in Mepal, Cambridgeshire.
Race-goers can expect a "fair bit of cloud" but will enjoy largely dry conditions, he said.
The best National Trust gardens to visit this Spring
The best National Trust gardens to visit this Spring
This quintessentially English house boasts stunning grounds with captivating views, a picturesque working watermill and wildlife discovery area. In the spring you can see daffodils fill the gardens while tulips pop up in the Himalayan Silver Birch grove. Visit the website for more information.
The Blickling Estate's 55 acre garden is one of the greatest in England and right at the heart you can find the stunning Jacobean hall. Visit in spring to see some of the best bluebells in Britain and if you fancy getting active there are around 500 acres of parkland and woods to explore on foot or by bike. Alternatively, try and find the Secret Garden for a moment of peace and relaxation in spectacular surroundings. Visit the website for more information.
At Bodnant you can admire the plants from all over the world that are visible in this garden thanks to seeds and cuttings collected over a century ago. Created with the help of five generations from the same family, this garden offers stunning views of Snowdonia and don't miss the Dell in spring which can be found hidden deep within the wooded valley. Visit the website for more information.
The world-renowned gardens at Sissinghurst were created by poet Vita Sackville-West and diplomat Harold Nicolson who fell in love with the outdoor space. The colourful, abundant planting in the garden reflects the romance and intimacy of Vita's poetry. In early spring, visitors to the gardens will see a carpet of colour thanks to the beautiful selection of flowers on display. Visit the website for more information.
Morden Hall Park is an oasis of calm in the middle of England's bustling capital city. The river meanders through the former deer park and the area is a haven for wildlife and the 2.5 acre garden is a great place to enjoy the outdoors with friends and family. Visit the website for more information.
This twentieth-century garden has a stunning collection of rare and important plants which create a burst of colour in spring. Each day you can enjoy guided tours of the spectacular gardens and be sure to look out for the camellias, magnolias, bluebells and rhododendrons that can be seen around the estate. Visit the website for more information.
At Hidcote you will be given the chance to see a diverse collection from plants all over the world. This unusual garden is divided into 'outdoor rooms', each designed with its own character. But the formality of the rooms slowly vanishes as you move through the garden, appreciating the plants and flowers that can be seen. Visit the website for more information.
Stourhead first opened in the 1740s and the landscape garden is known across the world for the magnificent lake, classical temples, mystical grottoes, and exotic trees. The azaleas, magnolias and rhododendrons burst into flower and really bring the gardens to life with their subtle fragrances and stunning colours. Visit the website for more information.
The three valleys of Glendurgan Garden are full of natural beauty and amazing plants. This sub-tropical environment blooms with magnolias, wild flowers and woodland flora. Once you've finished exploring the gardens you can take a trip into the maze that has been confusing people for 180 years. Visit the website for more information.
Known for being the National Trust's earliest flowering spring garden and boasts a host of spectacular plants and flowers to match. The shelter of the brick walls, and west Cornwall's mild climate, provide the conditions for more tender species to survive outdoors and you can experience plants from all over the world in this stunning garden. Visit the website for more information.
Clumber Park covers more than 3,800 acres and is a beautiful combination of parkland, heath and woods. The park gives you plenty of space to enjoy the open air and outdoors with friends and family while appreciating the beautiful walled kitchen garden and the longest avenue of double lime trees in Europe. Visit the website for more information.
Sizergh Castle is tucked away outside of Kendal in the countryside and the estate is home to 1600 acres waiting for you to explore them. Sizergh has expanded gradually over the past 300 years and if you visit during spring you will have the chance to see the brightly coloured tulips on the top terrace and walk beneath cherry blossom in the Dutch garden. Visit the website for more information.
This magnificent 12th century abbey was established by devout monks and the ruins that remain are a reminder of medieval life. The stunning water garden's moon shaped ponds and classical statuary were the vision of John Aislabie and his son William in the early eighteenth-century. Today little has changed, be sure to look out for primroses and wood anemones in the woods around the abbey. Visit the website for more information.
Wallington has been home to the unconventional Trevelyan family for many generations. The family loved being outdoors and the stunning house is surrounded by an informal landscape of lawns, lakes, woodland and farmland. Don't miss the hidden walled garden that can be found nestled in the woods and is home to Neptune's gate, a stone staircase, the Mary Pool and colourful borders of flowers. Visit the website for more information.
Rowallane Garden gives you the opportunity to let your imagination run wild among the unusual plants and flowers that can be found there. A mixture of formal and informal spaces, the gardens contain a treasure trove of exotic plants from all over the world and spring is often one of the most exciting times to visit as this is when the fantastic rhododendrons burst into colour. Visit the website for more information.