Just to precisely answer the question,
Was there a British tax for British citizens staying abroad in the fifties?
No, there was absolutely no tax.
The line of dialog is referring to the limit on how much could be spent abroad.
(Via the limit on exchanging currencies.)
Do note that furthermore, the limit mentioned was actually quite high.
Currency restrictions existed between 1939 and 1979.
The main goal of these restrictions after 1945 was to insure that enough foreign exchange was available to finance needed imports from non-sterling areas.
This meant that sterling currency that could be exchanged to foreign currency was greatly limited.
Starting 1945, this was £100 per year.
Between 1952 ...
I wrote this, then deleted it because it doesn't name the process and names were what the OP asked for. But no other (better) answer is around so far:
Traditionally, the feudal "contract" between peasants and the nobility often specified non-monetary goods and services, e.g.:
The peasant had to work so-and-so-many days on the lord's fields in ...