The short answer is no they didn't. The Royal Navy remained in Singapore until 1975, rather than leaving in 1971 as had been announced in 1968 (mainly due to a change of government in the 1970 UK general election).
The comment on Reddit is presumably referring to the announcement in January 1968 by the UK Labour government in the aftermath of the 1967 economic crisis, although this was hardly something intended to 'screw over' Lee Kuan-yew!
The problem for Singapore was both economic and military. The UK military presence provided almost all of Singapore's defence and military security. UK military spending in Singapore accounted for some 20% of their GDP. That accelerated withdrawal announced in January 1968 would undoubtedly have caused significant problems for the island had it happened.
In the event, the UK government initially extended the withdrawal deadline to the end of 1971. After the 1970 UK General Election, the new government then established the Five Power Defence Arrangements to provide for the security of Singapore and Malaysia. This included the UK agreeing to maintain a smaller military force in Singapore, together with forces from Australia and New Zealand, until the mid-1970s.
Timeline of events
The timeline of events was as follows:
This was an example of the UK government having to 'cut their coat to suit their cloth'. They had realised that the then-current levels of UK defence spending were simply not affordable, and changed their strategic priorities accordingly.
"package of measures including defence cuts, restrictions on hire purchase (credit), and higher interest rates"
16 January 1968: UK Government announced that troop withdrawals East of Suez would be accelerated due to the defence cuts announced in December.
18 June 1970: Edward Heath's Conservative government won the 1970 UK General Election
1971: The Five Power Defence Arrangements (FPDA) were signed by the UK, Australia, New Zealand, Malaysia and Singapore.
24 September 1975: HMS Mermaid. the last British warship based in Singapore left, and Her Majesty's Naval Base, Singapore, was handed over to the Singapore government which converted it into a commercial dockyard.
March 1976: The last British soldiers left Singapore.
1989: The last New Zealand contingent of the FPDA left Singapore.
The National Library Board of Singapore has a page on their website titled British withdrawal from Singapore, which has some further details and links to other sources which you might find of interest. These include a couple of articles from The Straits Times, dated 19 July 1967:
(click to enlarge)
and 17 January 1968:
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which covered the initial announcements by the UK government.
You'll notice from the second article that the the British Commonwealth Secretary, George Thomson, had also announced the UK's intention to negotiate an updated Anglo-Malaysian Defence Agreement (AMDA). These negotiations would eventually lead (under a new government) to the FPDA mentioned above.