I don't think so.
Why should a bank have to service anyone's account if they didn't want to ?
Because the law sets out the very limited grounds on which they may refuse a basic account.
"
22.—(1) A designated credit institution must offer a payment account with basic features to any consumer who—
(a)applies for a payment account with basic features on or after 18th September 2016; and
(b)meets the eligibility criteria set out in regulation 23."
Say you robbed a Lloyds Bank. I doubt they'd be happy to see you again.
That *might* come under section 25(2) depending on how the robbery took place.
But if it did not fall under that section, and the customer meets the other eligibility criteria, they cannot refuse.
"
25.—(1) A designated credit institution must refuse to open a payment account with basic features for a consumer where it would be unlawful for it to do so, including where opening the account—
(a)would be contrary to the Fraud Act 2006(
2)
(b)would be contrary to the Money Laundering Regulations 2007(
3);
(c)would be contrary to section 40(
4) of the Immigration Act 2014 (prohibition on opening current accounts for disqualified persons)(
5);
(d)would breach a requirement or limitation imposed by the Authority on the designated credit institution under Part 4A(
6) (permission to carry on regulated activities) of the Act that prevents it from accepting new customers.
(2) A designated credit institution may refuse to open a payment account with basic features where it considers that the consumer’s conduct in relation to the designated credit institution’s staff amounts to the commission of an offence under—
(a)section 4(
7), 4A(
8) or 5(
9) of the Public Order Act 1986(
10);
(b)the Protection from Harassment Act 1997(
11);
(c)section 38 of the Criminal Justice and Licensing (Scotland) Act 2010 (threatening or abusive behaviour)(
12);
(d)Article 9 of the Public Order (Northern Ireland) Order 1987 (use of words or behaviour or display of written material)(
13);
(e)the Protection from Harassment (Northern Ireland) Order 1997(
14)."