Weather forecasters say 60mph gales are expected in the run-up to Christmas Day, before 70mph winds hit from Boxing Day.
The Weather Outlook forecaster Brian Gaze told the Daily Mirror: "Storm Dylan has potential to be named over the Christmas period.
"Stormy spells are due. 60mph gusts and some snow risks are expected in the north leading into the pre-Christmas weekend, with winds picking up in the south with 50mph gusts possible.
"And after Christmas Day it looks like we're seeing stronger winds which could push 70mph."
Speaking to the Daily Mail, Met Office forecaster Helen Roberts said the south-east will remain chilly on Sunday but rain sweeping from the north-west will bring milder temperatures for other parts of Britain, including Central and Western England.
Ms Roberts added: "Monday is looking decent but not overly warm - a lot of sunshine and pretty much dry across the board."
Tuesday could see temperatures of 15C in England's south-west and the east of Scotland, before conditions turn windy from Thursday, with 55mph gusts affecting the north.
Met Office forecaster Mark Wilson told the Daily Mirror: "We could see windy weather for all of the UK at times up to New Year's Day.
"People travelling in the Christmas period should check the forecast and any warnings and take heed."
The UK's best Christmas markets
The UK's best Christmas markets
Traders from all over Europe and much further afield come to the Belfast Christmas Market at City Hall. Browse the selection of handbags, satchels, wooden toys, essential oils and hand-painted pottery. Don't miss the new food court for a bratwurst or Dutch pancakes. Dates: 18 November to 23 December 2017. Stay:The Merchant Hotel
Hosting one of the UK's largest Christmas markets, Manchester goes into full-on festive mode with several markets popping up in the city. Stock up on international food, traditional crafts, amber jewellery and ornaments. Dates: 10 November to 20 December 2017. Stay: Abode Hotel
Bringing a touch of Alpine charm to the south west, Bath Christmas Market plays host to more than 200 little wooden chalets brimming with locally made gifts and festive food. Set against the backdrop of Bath's Roman architecture, the city makes for one of the most atmospheric Christmas destinations in the UK. Dates: 23 November to 10 December 2017. Stay: Brooks Guesthouse
Leeds Christkindelmarkt is one of the most established German Christmas markets in the UK. Held in Millennium Square in the city centre, highlights include the Frankfurter Scheune at Alp Chalet - perfect for delicious Bavarian delicacies. Dates: 10 November to 24 December 2017. Stay:The Chambers Park Place
The Frankfurt-style Christmas market held in Birmingham is one of the biggest of its type outside Germany and Austria. Don't miss the live music, weissbeer and roasted almonds. Dates: 16 November to 24 December 2017. Stay:Hotel du Vin & Bistro
Set in Edinburgh's city centre against the backdrop of Edinburgh Castle, the Christmas markets include the ever-popular European Christmas Market with its delightful gifts and treats, and the Scottish Market which offers the best food, drink and craft Scotland has to offer. Stock up on unique chocolate, Gin, Scottish crafted jewellery and woodwork at the Scottish Market. When: 18 November 2017 to 6 January 2018. Stay:Sheraton Grand Hotel & Spa
Set against the beautiful backdrop of Exeter Cathedral, the Christmas market offers something for all, from handmade gifts to decorations and warm food. Although it is inspired by continental markets, it represents the best of what Britain and the South West has to offer. Stock up on crafts, unique gifts and decorations. Dates: 16 November to 17 December 2017. Stay: The Magdalen Chapter
Winchester Christmas Market is recognised as one of the best in Europe, attracting more than 350,000 visitors each year. Traditional wooden stalls are set up in the Cathedral's historic Close - a perfect setting for festivities.Stock up onBritish jewellery, glass and decorations. Dates: 20 November to 22 December 2017. Stay:Lainston House Hotel
Cardiff Christmas market is set in the pedestrian areas of the city centre, with stalls offering shoppers a range of quality craft products including enamel and pewter work, Welsh slate products, carved Welsh love spoons, metalwork, pottery, jewellery and traditional wooden items and toys. There is also a range of delicious seasonal food on offer, as well as plenty of mulled wine to keep shoppers warm as they go. Dates: 9 November to 23 December 2017. Stay:Jolyons
Winter Wonderland returns to London's Hyde Park in November with the ice rink, a giant observation wheel and, of course, its famous Christmas market. Enjoy hot cider, mulled wine and farmhouse foods alongside a spot of rustic revelry in the shape of an outdoor fire pit at the park’s heart. Dates: 17 November 2017 to 1 January 2018. Stay: Park Plaza County Hall
The luxury Christmas market in Nottingham's Market Square features 65 Victorian-styled trading cabins with an array of quality Christmas gifts from local traders and mouth-watering treats, timber decked walkways, an Ice Bar, a bandstand and at the centre of it all, an outdoor ice rink which promises to be bigger and better than ever before! Dates: 17 November to 24 December 2017. Stay:Jurys Inn Nottingham
This small, traditional market is set in the picturesque Whitefriars Square and is a good spot for quirky Christmas presents. Pick up traditional festive gifts, such as tin toys and Christmas ornaments, and enjoy German foodie treats, incudling Bratwurst and gingerbread. Dates: 25 November to 24 December 2017. Stay: Canterbury Cathedral Lodge
Gloucester's impressive historic docks provide the backdrop for a very Victorian Christmas experience. Explore an authentic market selling high quality food and drink as well as hand-made gifts. Enjoy choirs, brass bands and don’t forget to keep an eye out for a host of colourful and larger than life Dickensian characters who bring the market to life, all under the watchful eye of the faithful 'peeler'. Dates: 16 to 26 November 2017. Stay:The New County Hotel
The European-style St Albans Christmas Market offers a unique location in the walled Vintry Garden in the shadow of St Albans Cathedral. The market has more than 60 stalls selling a wide range of gifts and goodies, including decorations, jewellery, clothing and homeware. Festive food ranges from German-style bratwurst to gluhwein and there is packed programme of festive fun, including music, dance, magic and circus skills. Dates: 25 November to 23 December 2017. Stay:The Clarion Collection Hotel