WOW, ok practical advice time, firstly i will explain that i work for the leading credit reference agency in europe and there are a number of things you should do.
1- bare in mind that just because you have checked your credit report via equifax, this does not mean you have seen all the credit profile information available. Lenders have different contracts with different agencies.
To make sure you are not missing anything i'd advise you to register with 2 others CallCredit & Experian/CreditExpert. This will help you make sure that there isn't any other information out there you are unaware of.
2- Once you have registered with the above agencies (including Equifax) i'd advise you to contact each of them and request to put a NOC password on your credit profile (notice of correction password), this password would need providing for every credit application made in the future within your credit profile and help prevent any further damage.
3-
CIFAS - go to there website, read up and register too, they will help you with advice and guidance in having this fraudulent activity stopped and resolved.
4- You have already contacted the police, i'd advise to contact your existing bank/companies that you have agreements with (if you have not already) also contact any companies you have seen on your credit reports and start the investigations process.
5- I know its hard, but be positive, The credit reference agencies are there to help you, they will have fraud depts and advisers who will be able to advise and assist you, Credit ref agancies can also help get your credit profile corrected if fraud is prooven.
Hope this helps, need any advice, just trust msg me
Richard