Q:

Did Britain borrow $120 billion in 1945?

This copy-paste has being doing the rounds of local newspaper letters pages and dodgy hard-core pro-Brexit Facebook pages, etc:

JEAN Claude Juncker should be forced to walk past every white gravestone in Normandy and the rest of Europe to say a personal thank you to all of the British, American and Commonwealth soldiers that gave their lives, so that Europe could be free. 
He should also be reminded that Britain borrowed $120 billion dollars in 1945, to fund this freedom and this took the British taxpayers 61 years to repay it back. 
I therefore suggest that EU pay this figure first, along with all the interest we accrued, then we can talk about paying our share of his ‘bar bill’.

(Followed by a local address)
Skipping the political issues, the closest reference I could find was the Anglo-American Loan of 1946 of around $5 billion which took 60 years to pay back. Were there other loans, or how could $5 billion become $120 billion?

A:

the closest reference I could find was the Anglo-American Loan of 1946 of around $5 billion which took 60 years to pay back. Were there other loans, 

No, there weren't any loans that could approach that figure. Something of this magnitude would not have escaped the history books, and ultimately Wikipedia. It's not like they were borrowing in secret from the Ferengi.

or how could $5 billion become $120 billion?

One can only speculate since no real argument is given, just a figure. If one were really predisposed to come up with a big number, they could take the total amount repaid (with interest) "$7.5bn (£3.8bn) to the US and US$2bn (£1bn) to Canada" (according to Wikipedia) and further multiply this $9.5bn by the same factor that Wikipedia uses to give a 2017 equivalent (i.e. inflation adjustment) of the initial loan. That factor is around 13.3 derived from "$US 3.75bn (US$50 billion in 2017)". And 13.3 times $9.5bn gives a figure of $126bn. But this is grade F economics... because to compute a proper present value you need to take into account the schedule (i.e. dates) of repayments, the value of each, the exchange rate at the time, to finally come up with an adjusted value. I'm not aware of such a properly made calculation (and I won't venture one myself)...
I suspect however that correct total amount (adjusted for inflation) repaid by the UK on this loan might even be below the (inflation adjusted) intial loan value, from the US at least, because the 2% interest that the UK paid on the loan is mostly below the annual US inflation ratio in this post-WWII period, i.e. the real interest rate on the Anglo-American Loan was probably negative.
Another possibility as oerkelens suggested is that the statement in question confused the Anglo-American Loan with the later Marshall plan... which came later (1948) and didn't all go to Britain, although the total amount for all countries was $13bn, or approximately $140bn adjusted for inflation. Of the initial sum, only $2.7bn went to the UK which in 2017 would be $29bn. Even if we add this to the 1945 loan (again adjusted for inflation) we don't exceed $80bn from the US to the UK in 2017 dollars.
I think however that the post in question was talking only about the 1946 loan because that's the one that took ~60 years to pay back.

Ed Balls, the Economic Secretary to the Treasury, said: "This week we finally honour in full our commitments to the US and Canada for the support they gave us 60 years ago.

And the Marshall plan money didn't have to be paid back:

Most of the countries that received Marshall Plan money assumed they would never be asked to repay it. Over time, Britain, France and the others simply absorbed the funds into their national budgets.

