Not knowing exactly what the will says it is hard to comment with precision. (I am a solicitor but not a probate one, lol!)
However, it sounds as if (aside from the cash bequest to you) the GM left the remainder of her estate to be split between your Dad and Uncle, with your Dad's share being held in trust for him by your Uncle and an allowance paid from it.
The allowance is likely to have been limited in some way - often it is any income earned by the trust (interest, rent etc) and as your Uncle retained the property until recently, it is likely that any allowance was paid only from your Dad's share of the liquid (cash) estate, leaving the half share of property equity intact. (It is possible that your Uncle may have mortgaged the property to release further cash sums to your father, which would have eaten into his share but I am just speculating here.)
It is likely that some or all of your Dad's share of property equity remained at the time of his death and that has now been liquidated by your Uncle on the sale of the house, of which he was (presumably the legal owner.)
There are a number of possibilities.
Your best chance (legally supported) would be if your GM will also specifies what is to happen to your father's share after the trust is dissolved i.e. upon his death. This is referred to as having a "life interest" rather than a complete entitlement to the estate. She may have specified that any remaining sum passes to you (good) or Uncle/someone else. If this is the case, i.e. that you are entitled to the reversion, then your Uncle as trustee/executor is obliged to discharge the proceeds to you. Provided the will names you in this way, your adoption is irrelevant.
If the will does not state what happens to your Dad's share once the trust dissolves, then it depends on whether he left a will and therefore if you are the named beneficiary. You do not think that he did so I assume this is correct.
If no will then he died intestate. His share will therefore pass to any offspring (unfortunately as you were adopted your legal relationship to your father will be considered severed). If no offspring, then to surviving parents (I think, but I presume there are none). If no parent then to siblings. Assuming your Uncle is the only sibling he will probably get the lot and anything he chooses to give you will be a voluntary gift only.
The HMRC debts complicate things as creditors are entitled to be paid out of the proceeds of the deceased's estate before the beneficiaries. So if you or your Uncle are beneficiaries you will probably have to pay HMRC what is due. However, if your Dad only had a "life interest" in your GM's (half) estate then arguably his estate is limited to the income/fixed allowance which presumably he spent. The remainder of "his" half of GM's estate (called "the reversion" in probate law) is protected in this case I THINK but if this seems to be the case, this is where a probate lawyer would be very helpful to you, to make sure the creditors are dealt with correctly so there are no nasty surprises.
Good luck OP. I think the most helpful thing I can say is that its important to know exactly what your GM will says. If it is not in your favour then fingers crossed your Uncle might be generous.
One last thing, you mentioned that your Dad owed your Uncle money so he may also be a creditor who would be entitled to claim such sums (provided that he can evidence them) before the estate is distributed, either legally or by way of gift.