In brief, there are three types of firm: the factoring arms of the major clearing banks; large, specialist firms; and small, specialist firms. Each will have its own criteria as to what sort of customers it wants: some will dislike exports, or companies beneath a certain size, or companies without a positive net worth (net assets of more than £0). As with most things, it is worth shopping around a bit to find which one is the right fit for your company.
In general, the smaller factoring firms are probably more flexible than the larger ones, and may also prove cheaper. The flexibility will come in handy if your business is slightly unusual in some ways, perhaps in having some export clients or in its terms of sale. The larger firms will have more strict rules, and less ability to disregard them.
An introduction is often the way people find their factoring company and your bank manager is probably the most common source. You may find that your bank is happier to continue overdraft or other funding facilities if you use their factoring arm than if you use an independent firm, though try not to be bullied into paying higher fees or getting less good service than you deserve.
Smaller factoring firms are probably more flexible than the larger ones, and may also prove cheaper.
Above all, do negotiate. Most of the elements of the factoring agreement can be negotiated in practice: the service charge percentage, the minimum guaranteed fee, the interest rate, and the percentage advanced against each invoice.
There are a number of brokers who will advise you on the right firm for you; these firms usually receive a payment from the factoring company as an “introduction fee” so check to see that the advice you receive will be independent.
The Asset-Based Finance Association (ABFA) is the UK's member body for companies that offer services such as factoring and invoice finance. If you are looking for a list of companies that offer these services then you can obtain one from their member pages. Members of the ABFA sign up to a code of practice which insists that they must be fair, professional and honest in their dealings. Therefore, you might wish to check that the company you are looking to do business with is a member of the ABFA rather than one which isn't.