The first question has to be 'Are you sure that he left a will?'. If he didn't, and died intestate, then any illegitimate children are each entitled to the same share of his estate as his legitimate children - but the estate has to be valued at more than a quarter of a million pounds or they'll get nothing anyway. (Up to that amount his wife would get everything). See the chart here for an explanation of the intestacy rules:
http://www.tollers.co.uk/system/docs/178/original/Rules%20of%20Intestacy%20Flowchart.pdf
(It's actually possible to challenge the intestacy rules, as below, but that's probably far harder than challenging a will).
If your biological father did leave a will he was entitled to include or exclude anyone he liked (or disliked, as the case may be). He could leave everything to Battersea Dogs' Home if he so chose. It would then be up to anyone who thought that they should have received some benefit from the will to challenge it if they chose to do so.
Any his children (irrespective of legitimacy or otherwise) can apply "for an order . . . [varying the will] . . . on the ground that the disposition of the deceased’s estate effected by his will or the law relating to intestacy, or the combination of his will and that law, is not such as to make reasonable financial provision for the applicant"
Section 3 of the relevant Act lays down the matters a court must have regard to when deciding whether to grant such an order:
http://www.legislation.gov.uk/ukpga/1975/63
You may well have a legitimate claim but you should be warned that plenty of legal battles over such matters have ended with the entire value of the estate being swallowed up by legal fees. A good solicitor would probably start by seeking to get the existing beneficiaries of the will to voluntarily give part of their inheritance to you, in return for you agreeing not to pursue action through the courts. A bad one might simply start building up lots of legal expenses straight away. Proceed with caution!
Chris