I see this claim raised and shared by “friends” on facebook (often sharing some nationalistic posts), and I tried to find some facts online but can’t see any reliable source.
Did Britain ask Poland to pay such money? (And if it did, why? Polish pilots were defending the UK borders at that point and are held in high respect here in Scotland)
And if it did, did Poland pay that sum?
In short, no. In long, nooo. But there's context.
The claim in question is frequently raised by contemporary Polish nationalists. Trying to find out why they would utter falsehoods (or if they do it knowingly) is likely futile, but contemporary Poland is somewhat obsessed with reparation payments, with the possibility of asking Germany to pay reparations for damages done during World War II being a frequently presented political opportunity, particularly by Polish conservatives that frequently find themselves at odds with contemporary German policy since the early 1990s. That is in spite of Poland agreeing to waive any right to demand reparations from East Germany in 1954, a responsibility/privilege that carries on to the FRG after Germany was united in 1990.
But alas, that just for context that this is not all that out of the ordinary. Reparations are a popular talking point, and the idea that Poland saw itself at the end of such reparations without justifications provides a better moral justification for Poland itself to demand possibly unreasonable reparations from other nations, primarily Germany. Polish legal claims to possible German reparations to Poland rely solely on the question whether 1954 Poland was in fact acting on behalf of the Polish people or was merely a Soviet agent, making the agreement of 1954 more of an agreement between East Germany and the USSR rather than East Germany and Poland.
The answer to your question can be found in the Treaty about finances between Poland and Great Britain and Northern Ireland of 1946.
I will try to bold anything relating to the question of war payments. I will have to make changes to the text where I cannot replicate the icon for pound sterling (a currency-version of L), otherwise the text will remain as presented, with the exception of articles I deem irrelevant to the question at hand.
Article I
The Government of the United Kingdom will make no claim for repayment of 73 million sterling, in respect of amounts spent on war material, equipment, supplies, etc, for the Polish Armed Forces in the West.
Article II
The Government of the United Kingdom will leave in abeyance at present the question of the repayment of the Military Credits, amounting to a further 47 and a half million pound sterling, expanded on the salaries and pay of the Polish Armed Forces in the West up to the 5th July, 1945, but reserve their right to reopen discussion of this question.
Article III
In discharge of all claims made by the Government of the United Kingdom in respect to the Polish civil administration including welfare and educational services in the United Kingdom, and the maintenance of the Polish refugees in various countries overseas, for which the Government of the United Kingdom advanced the sum of approximately 32 million pound sterling, the Polish Provisional Government agree to pay and the Government of the United Kingdom agree to accept immediate payment of 3 million pound sterling in gold and 10 million pound sterling to be repaid by equal annual installments of 666,666 pound sterling over a period of 15 years, the first payment to be made 5 years after the date of the entry of this Agreement into force.
[...]
Article V
(1) In addition to the Polish assets which they have already transferred to the Polish Provisional Government, the Government of the United Kingdom will, subject to the provisions of paragraph two of this article, arrange for the transfer to the Polish Provisional Government of all assets of the former Polish Government which were acquired before the 1st June 1946 out of monies advanced by the Government of the United Kingdom.
[...]
Article VI
The Government of the United Kingdom will transfer to the Polish Provisional Government free of charge surplus goods to the value of 6 million pound sterling, now at the disposal of the Government of the United Kingdom to be selected by representatives of the Polish Provisional Government from lists to be made available to them by the Government of the United Kingdom. It is understood that the 6 million pound sterling is inclusive of transport, insurance and other charges which may be incurred in dispatching the goods to Poland, but in the event of the Polish Provisional Government themselves paying these charges the quantity and value of the goods to be made available under this clause shall be correspondingly increased.
So there you go. The UK won't charge the PPG for the equipment used by Polish soldiers, it for now won't charge the PPG for the salaries paid to Polish soldiers (and to my information never did afterwards), it will charge the PPG for the care provided to Polish refugees in Allied territories, and the UK agrees to return any and all assets of the former Polish government.
All in all, not a bad deal for Poland.
Your question, specifically concerned with equipment, airfield and petrol, would be covered by Article 1 of the treaty. Britain chose to not charge the Polish side for British war equipment, merely for civilian care as well as holding themselves open the option of charging Poland for military salaries paid to Polish individuals in the British armed forces. Neither of these categories is concerned with the petrol inside British military aircraft.
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