HMS Dreadnought, HMS Warspite, HMS King George V. Ships one would imagine would almost certainly be turned into museums, yet they were all scrapped instead. There isn't a single Royal Navy battleship in existence today. There is only one British-built battleship, the IJN Mikasa in Japan.
Even outside battleships, its similar. RMS Olympic, sistership of RMS Titanic, was also scrapped.
Considering how they have done, it is nothing short of a miracle that HMS Victory still exists. So why is this the case? Why do the British just scrap so many of their historically significant ships?
To put it simply, scrapping a warship is a way to make money, while keeping them as a museum costs a lot of money. For the UK scrapping ships served to raise funds for the government, provide jobs in the ship-breaking industry, and provide scrap metal to help industry recover. Meanwhile, it was never clear whether or not museum ships would break even, let alone make a profit.
Let's look at the British ship-breaking industry following WWII. This was handled by a government body called the British Iron & Steel Corporation (Salvage) Ltd or BISCO, which also handled the supply of other raw materials to the steel industry. Ships the Admiralty no longer needed were handed over to BISCO. BISCO would then assign the ship to a suitable breaker's yard, where the ship would be scrapped. Following this, the scrap would be sold, the costs of the demolition returned to the breaker and the remainder of the money returned to the Government. This brought in a lot of money- in 1945 pounds, scrapping a battleship would bring in £450,000, while scrapping a destroyer would bring in £30,000 ($26,000,000 and $2,000,000 respectively today). You also need to factor in the reduced costs to the Admiralty, as there was no longer a need to man or maintain the scrapped ship. This also produced a lot of scrap. Annual output from the British ship-breaking industry was about 500,000 tons, or about 3% of the output of the British steel industry. For a nation like Britain, whose industry had been devastated by the war, and which owed the US and Canada £3.8 billion (again in 1945 pounds), this was an attractive option to increase revenue and rebuild their industry.
Meanwhile, repairing and restoring ships for use as museums costs a lot of money, as does maintaining them in good condition. In 1978-79, a British charity purchased HMS Warrior, the first true ironclad, which had spent 52 years as an oil barge. Restoring her to her original condition cost close to £8 million in 1979 pounds, or ~$52 million today. Restoring HMS Victory in 1922 was estimated to cost £16,000 for just the most essential repairs, while restoring her to her condition at the time of Trafalgar would cost £160,000 (1922 pounds). Converting this to today's money, this is ~$1,250,000 for essential repairs or ~$12.5 million for the full restoration. This money had to be raised by public subscription by the Society for Naval Research, launched in 1921. The more recent restoration of HMS Caroline, a WWI-era light cruiser, cost about £15,000,000 ($20,000,000) in today's money. Beyond the costs of restoration, there is the cost of ongoing maintenance. While paying visitors can pay this off, warships are expensive things to keep going. In the early days of HMS Belfast's career as a museum ship, there were recurring worries about whether or not visitor turnover would pay for the costs of dry-docking her when necessary. The experience of Victory is also illuminating; it took two years for the Society to raise £30,000. Most of the repairs were only possible due to a donation of £50,000 by the shipping magnate James Caird. If such donations were not forthcoming, then ships would not be saved.
Since repairing and restoring a comparatively small warship costs as much as was recouped by scrapping a battleship, it's easy to see why Britain chose to scrap most of its battleships.