The BASIC rules that apply are as follows (but see below):
If the value of your father's estate was greater than £270,000, then your father's children (including you, obviously) get to share half of the excess above that figure. (e.g. if the estate was worth £350,000, it exceeds £270,000 by £80,000. Your step mother gets £40,000 from that, plus the £270,000, with your father's children (but not stepchildren) sharing the remaining £40,000.
If the value of your father's estate doesn't exceed £270,000, your stepmother gets everything.
(See here:
https://www.hughjames.com/documents/docs/2020/intestacy-rules-flow-chart-february-2020-6443.pdf ).
HOWEVER the full value of the house will only form part of his estate if his name was the only one on the title deed.
IF your father and your stepmother owned the house as 'tenants in common', then your stepmother will retain her share in the property but the other half will form part of your father's estate. (She might still end up with all of it though, depending upon whether or not the total value of his estate then exceeded £270,000 or not).
HOWEVER if your father and your stepmother owned the house as 'joint tenants', then (as the surviving tenant) your stepmother now AUTOMATICALLY owns the whole property. (Intestacy law becomes totally irrelevant under such circumstances).
What all of that lot actually means to you is as follows:
IF the property was owned by your father and stepmother as joint tenants, then it now belongs entirely to your stepmother and she's free to leave it to whomever she likes in her will. There's no way that you can challenge it.
OTHERWISE it's
possible (but not necessarily advisable) for you to apply to a court to vary the normal intestacy rules on the grounds that they result in you failing to receive 'reasonable financial provision' from the distribution of the estate:
https://www.legislation.gov.uk/ukpga/1975/63
However such an application is a big (and potentially very costly) step. You'd definitely need to seek the advice of a solicitor who specialises in such matters before doing so. (I suspect that his/her advice might well be that, given the relatively small size of the estate, it might not be worth proceeding with such an application, even if he/she thinks that there might be some merit to your case).
You can download a copy of the title register for the house for £3 from the Land Registry website. (I'm assuming that it hasn't yet been amended after your father's passing):
https://www.gov.uk/search-property-information-land-registry
If the title register only shows your father's name, then (obviously) he was the sole owner. If both names are shown though, you need to look under 'Proprietorship Register' to see whether there's a statement along these lines shown there: “No disposition by a sole proprietor of the land (not being a trust corporation) under which capital money arises is to be registered except under an order of the Registrar or the Court”. If it's present, then your father and your stepmother were almost certainly 'tenants in common'. If not, then they were almost certainly 'joint tenants'.