Both parts of the claim are correct (if you define 'poor' as having a low GDP per capita).
As pointed out in other answers and in the comments, the UK had the third lowest GDP per capita out of the EU-9 in 1979 -- more than Italy and Ireland but less than Luxembourg, Denmark, the Netherlands, Belgium, France and West Germany. Here's a table
According to historic tables of EU revenues and expenditures, they were also the second highest net contributor to the budget in 1979. According to the table on page 94 of the linked report, the UK made a net contribution (total revenue minus total expenditure) of 1485.6 million ECU (European Currency Units; a unit of accounting) while West Germany paid a net of 1491.7 million ECU. Each of the other 7 member states made lower net contributions than the UK.
Even adjusting for population the UK would have been one of the highest net contributors at the time. Four of the nine member states in 1979 were net recipients. France made net contributions of just 79 million ECU (5% of the UK's) although its population closely matched that of the UK in 1979 (55 and 56 million, respectively).
The imbalance was considered so stark that the UK eventually managed to negotiate a significant and permanent rebate on its contributions to the EU budget.
The independent House of Commons Library (a research body for the UK parliament) has produced a number of reports on the topic in the context of Brexit. On the rebate, it says:
The rebate was introduced to address the issue of the UK making
relatively larger net contributions than other Member States. When the
rebate was introduced, in 1985, the UK received relatively little from
the EU budget: it had a small agricultural sector, but most EU
spending went on agriculture. At the same time the UK made
relatively high contributions to the budget, despite being among the
less well-off Member States at the time.
The European Parliament Research Service has an even more in-depth briefing on the imbalances in contributions and the origins of the UK's rebate:
The question of the UK's budgetary imbalances has been a source of
debate and friction since the country joined the then-European
Economic Community (EEC) in 1973. It was also one of the main topics
under the spotlight during the June 1975 referendum, when UK voters
supported continued EEC membership.
The historical context helps to understand the issue, which relates to
a number of features of the UK economy and the EEC's finances in the
1970s and 1980s. On the one hand, the UK had a small agricultural
sector, whereas most Community spending went on agriculture (some 70%
in 1984- 1985).
On the other hand, the system of financing of the Community budget,
which was then being implemented progressively, had as its main source
of revenue an own resource related to Member States' VAT bases,
alongside customs duties. In the UK, the VAT base in comparison with
gross national product (GNP) was proportionally higher than in other
In addition, the UK was more open than other Member States to trade
with non-EEC countries.
The combined effect of all these factors was a structurally negative
budgetary balance for the UK, which at the time was among the less
well-off Member States, with a per capita income lower than the EEC