You need to go to a branch of THEIR bank, HSBC.
You will need to fill in a 'Paying In Slip' (they'll have some available) on which you need to state:
1. The 'sort code' of THEIR branch of the bank;
2. THEIR bank account number
3. The name of the account you are paying it in to
4. The amount of the cheque
5. Who is paying it in.
At the bank counter, they will take the cheque and paying in slip, check the amount is correct, stamp the counterfoil (tear off strip from the paying in slip) and hand it back to you as proof of pay-in, and then they'll keep the cheque for processing. Later, the bank will process the cheque, put the money in the account you wrote on the paying in slip, and forward the cheque to your firm's bank where they will knock the money off your firm's account. This last stage may well be automated these days.
The account holder MAY have a paying in book for their own account (less common these days), but you won't have one for their account.
Payment on-line is much easier but you did ask about cheques so that's how it's done.