Yes they do, but from 2013-2018 they did not provide a significantly higher rate of interest in comparison to the highest yielding easy access Cash ISA accounts. In September 2018, the best fixed rate Cash ISA (Paragon Bank) is paying 1.55% for a fixed period of 1 year, and the best easy access Cash ISA (Virgin Money) is paying 1.35%. The biggest drawback to fixed rate Cash ISAs: is that they have a withdraw penalty if the saver decides to remove their money -- in 2018, this withdraw penalty varied from a loss of 90 days' interest to 270 days' interest. Easy access Cash ISAs do vary in their withdraw options: some allow unlimited withdraws (Shawbrook Bank) and some only allow 2 or 3 withdraws before a penalty is implemented (Virgin Money).
The biggest strength to fixed rate Cash ISAs is due to the fact that the interest rate is fixed, and savers will know the exact interest income they will receive over a 1, 2, 3, 4 or 5 year period. Easy access Cash ISAs on the other hand come to two varieties: those with a fixed rate bonus period and those without a bonus. The account bonus is usually for 1 year and is typically 1%; this ensures that this type of easy access Cash ISA will have a reliable rate of interest over a period of 1 year. Easy access Cash ISAs without a bonus are based on a flexible rate of interest, which means the bank can change the interest rate whenever they wish; this has the potential of going up or down depending upon the Bank of England base rate and general wider economic factors.
One overall drawback to Cash ISAs -- as a concept -- is that the UK government changed the rules on savings income tax on the 6th April 2016. The new rules introduced a tax free 'Personal Savings Allowance' and increased the threshold (based on the annual taxable income of an individual) for when people begin to pay tax on their savings income. That said, for higher income individuals, the Cash ISA is still a great way to save tax free.
At present the best fixed rate Cash ISAs are: 1 year Paragon Bank 1.55% (minimum savings £500); 2 year Shawbrook Bank 1.75% (minimum £5,000); 5 year Coventry Building Society 2.3% (minimum £1). Some other notable providers of a Cash ISA -- which are the close to the interest rate of the aforementioned products -- are: Ford Money, Leeds Building Society, Skipton Building Society, Sainsbury's Bank, and theAA.