The only reason that the Government budget is overstretched is that too may people and organisations are paying too little tax! The restoration of the 60% super-tax bracket would help, as would the establishment of an 80% 'greedy bastards' tax bracket. The removal of charitable status for churches and other religious organisations, as well a private schools, the abolition of tax relief on private education and healthcare fees, as well as 'non-dom' status would more than pay for a lot of stuff. Closing the offshore assets loophole and making all those wealthy, Tory-voting expats and tax exiles pay up!
Anyway most of these expeditions were financed privately. Back in the days when wealthy people were prepared to take chances to expand their business, rather than just scream for lower taxes and less regulation.
Elon Musk and his suggestively-shaped rocket are all very well, but if he was serious, he could afford to set up a moonbase just to look around and see if there was anything there worth digging up and sending back to sell. Goes double for Mars.
The saddest thing about it is that the British space programme was well in advance of the US one. So much so that the US government threatened to demand immediate and full payment of all war loans unless it was shut down! That was the second time that happened. In 1946, under pressure from IBM, the US forced the UK government to dismantle. and destroy the blueprints of, Colossus - the first true electronic computer - designed and built by Alan Turing at Bletchley Park. That's the only reason why the Stars and Stripes is on the Moon rather than the Union Jack!