you should renew the name immediately, otherwise you'll lose your registration, and the name will become available to anyone.
You don't mention which high level your domain name belongs to, but in the case of Nominet assigned names the suspension periods following registration expiry are as follows:
Seven days after registration expiry you (or the billing contact whose name is recorded on the registration) will receive an invoice from Nominet, which must be paid within a further 30 days if renewal is to be guaranteed. At the end of the 30 days the name will go into a 60-day suspension period. Once that period expires the name will become available to anyone (including you) for a new registration.
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