Cockroaches in the UK are usually associated with food premises, have you got a restaurant or cafe adjacent to the flat, if so, you will need to get your landlord to approach the owners, or contact environmental health and explain the situation.
If this is not the situation, you will need to bring in a Pest Control company to sort this problem, a Cockroach infestation is not a problem you can tackle yourself, believe me, I'm a pest controller and we have a problem eradicating these things ourselves sometimes.
I cant give you much idea of cost as I don't know the situation but likely to be well over �100.00 and could be an ongoing problem, especially if they are coming from an adjoining property.
Good luck