Savings rates have slumped since the Bank of England base rate fell to 0.25%, figures show.
According to Moneyfacts.co.uk, the average easy access savings account on the market paid 0.54% just before the Bank of England base rate was cut from 0.5% to 0.25% in 2016. Now it pays just 0.4%.
As well as the low base rate, schemes such as funding for lending have been blamed in recent years for depressing savings rates further, as banks have been less reliant on needing to attract savers' cash with attractive rates.
But Rachel Springall, a finance expert at Moneyfacts, warned that, even with a base rate rise, savers may not necessarily see much improvement.
She said: "Savers would do well not to jump the gun, thinking that this will be passed on to them or cause rejuvenation in the market.
"This is due to the fact that the link between base rate and savings rates has generally been severed over the years thanks to government lending initiatives.
"There is also no guarantee of a rate rise to be passed on in full or at all for some savings accounts, but a customer with a variable rate is more likely to see a change."
Ms Springall said challenger banks which are keen to attract savers' deposits have been helping to inject some competition into the savings market.
"Savers can get 1.3% with easy access with brands such as RCI Bank and BM Savings," she said.