Yes - transfers between all types of ISAs are allowed.
Please note that this is subject to the terms of the account you wish to transfer into accepting transfers in, and also checking the account you are transferring from, for any charges transferring money out - for example during the middle of a Fixed Rate cash ISA term.
Transfers for the current tax year must be made in full but you can transfer as much or little as you like from previous tax years.
You may also transfer as often as you wish, once again subject to the terms of your existing and new accounts.
You can complete an ISA transfer (opens in a new window) as part of your ISA account opening or after it's open.