You can buy up to Flex or PY and then purchase a pass to the lounge for $50/$25. From Tango this is likely very expensive. But ... I have seen PY offered for below Tango prices, once.

LHR lounge is worth $25 imho, $50 perhaps not - unless you wish to and can safely imbibe and operate under large quantities of alcohol.

Your only other option is either a different lounge of try posting in the lounge thread to see if anyone would guest you in. Given you are looking for LHR though I'm not sure you'll find anyone routing through at the same time. I didn't when I requested it on a Flex ticket not being willing to spend $50. I seem to recall the airport wifi was decent though and I instead got a meal just before security (acceptable lamb shank overlooking the planes for what it's worth). Can't recall the place but it was at the far right of T2 as you enter.