Factbox - UK local government elections: Key results and ones to watch

LONDON (Reuters) - Prime Minister Theresa May's Conservative Party avoided a wipeout in London local elections and eked out gains in Brexit-supporting regions elsewhere, results on Friday showed, denting the opposition Labour Party's hopes of a big win.

Below is a list of some facts about the elections and five council results that set the tone for the overall outcome.

- Councils are the local government authorities with responsibility for providing public services that affect residents' day-to-day lives. They are made up of varying numbers of seats, and run by the party that has an overall majority of those seats.

- More than 4,000 council seats are being contested, determining the make-up of 150 councils. More than 40 percent of the seats are in London.

- All 32 London boroughs are electing their whole councils. Some councils outside London are only electing one-third of their councillors this time around.

- Unlike national elections that decide seats in parliament, or the 2016 EU referendum, Thursday's elections are open to EU nationals registered and resident in electing boroughs.

RESULTS

PETERBOROUGH - RESULT: CONSERVATIVE GAIN

The Conservatives won the single extra seat they needed to take overall control of this council which represents an eastern area that voted 61 percent to leave the EU. The anti-EU UK Independence Party lost its only seat on the council as part of a broader collapse in the party's vote.

TRAFFORD - RESULT: CONSERVATIVE LOSS

A council in the northern city of Manchester which had been the Conservatives' highly prized foothold in a region dominated by the opposition Labour Party. The Conservatives lost five seats, while Labour gained four, leaving the council without a single party in overall control.

WANDSWORTH - RESULT: CONSERVATIVE HOLD

A hotly contested Conservative borough in southwest London with a tradition of low taxes dating back to former prime minister Margaret Thatcher. Labour gained seats on the council, but the Conservatives held enough to keep control.

WESTMINSTER - RESULT: CONSERVATIVE HOLD

The Conservatives lost three seats on this symbolic council at the heart of London's political district but retained overall control by a wide margin. It has been run by the Conservatives since its creation in 1964.

BARNET - RESULT: CONSERVATIVE GAIN

The Conservatives regained overall control of Barnet council, having previously been the largest party there, but just short of a majority. The borough was a big target for the Labour Party but a row between Labour and the Jewish community over the handling of anti-Semitism in the party looks to have hit their vote.

Barnet has the highest proportion of Jewish residents in England at 15.5 percent, according to the latest census data.

(Reporting by William James; Editing by Kevin Liffey)