The sort code 62-30-88 does not belong to a branch of a high street bank. Usually, codes that start with 62 belong to the NatWest, but this code appears to belong to an online company called Card One Banking.
If you think the bank you were after is a branch of NatWest, then the nearest sort code to the one given is 62-30-86, a NatWest Credit and Collection Clearing facility at Goodmans Fields, PO Box 114, 74 Alie Street, London, E1 8HL. Telephone: 207 4802345.
Card One Banking
This is not a bank, but an Authorized Payment Institution, and is part of the Spectrum Financial Group Ltd. Once you set up an account with this company, they provide you with an account number, and a sort code, with the latter presumably on a geographical basis. They can be contacted at PO Box 3634, Chester, UK, CH1 9NL or by phone on 0871 811 1881.