No seats changed hands in this week’s six council by-elections, though there were a few intriguing swings to give the main parties something to ponder.

Carlisle is a key target for Labour at the general election, but in two by-elections in the Castle ward of the city there was a swing from Labour to the Conservatives.

One of the contests was for a seat on Cumbria county council, and although Labour held the seat, there was a hefty 7.9% swing to the Tories.

The other was for a seat on Carlisle city council, and again though Labour held the seat there was a swing to the Conservatives, albeit of a more modest 1.1%.

The parliamentary constituency of Carlisle is currently held by John Stevenson for the Tories, who won a majority of just 853 in 2010. Labour has a majority of six on Carlisle council, and a swing of 1% would see them gain the constituency at the general election. It’s the kind of seat Labour simply has to win if it wants to overtake the Tories and become the largest party in the House of Commons – let alone form a majority government.

Elsewhere on Thursday, Labour retained a further two council seats.

One was in Newham in London, where the party continues to enjoy the dubious honour of holding 60 out of 60 seats.

The other was for the Ollerton ward of Newark and Sherwood council. This result saw a swing of 5.3% from Conservative to Labour, and will be worrying to Tory chiefs. Sherwood is an ultra-marginal where Conservative MP Mark Spencer has a majority of only 214. A tiny swing of 0.2% would see Labour take the seat.

There was some solace for the Tories in the nearby Collingham and Meering ward of Newark and Sherwood council, where they held a seat. There was an 8.7% swing to Labour, though this needs to be put in context: Labour came fourth, behind the Tories, an independent and Ukip.

The final by-election this week brought cheer for the Lib Dems. They defended a marginal seat in Abingdon Dunmore on the Vale of White Horse council, a ward where the other councillor is a Tory.

The Press Association’s analysis of all six comparable results suggests a 1.4% projected Labour nationwide lead over Tories.