Answer: It is likely that you have signed an assured shorthold tenancy agreement and if you do not end the tenancy properly you could be liable to pay rent for the whole of its term. Check carefully the terms of the agreement, which is likely to be a tenancy for a fixed six or 12 months — in which case, really, you are stuck.
Sometimes a landlord will agree to keep any deposit paid in advance, which may very well equate to a month's rent. Provided he or she is also reimbursed for any expenses they or their letting agents have incurred, the landlord may agree to release a tenant if a replacement can be found. In your case, although you may consider that the landlord is asking for a lot of money, he is entitled to ask for all the rent due under the terms of the tenancy agreement.
Accordingly, if he is asking for £675 — which is possibly the deposit you have paid — and is not asking you to pay anything else, then it would seem sensible to agree to this. Make sure that you receive something in writing from the landlord confirming the tenancy has ended.
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These answers can only be a very brief commentary on the issues raised and should not be relied on as legal advice. No liability is accepted for such reliance. If you have similar issues, you should obtain advice from a solicitor.