Generally, the answer for this is yes, and you can still access your transaction history for closed accounts as long as you have a registered account with your bank. However, how long you can access it after you have closed your account differs from bank to bank. According to UK regulation, banks need to give you access to up to 5 years of your transaction history at current account closure.
Usually, accounts which have been closed due to fraud or other unlawful activity, impairment or which have had no activity in a long while will not be eligible to receive transaction history.