SNP politicians at Holyrood and Westminster have written to Cllr Cammy Day, the leader of the Edinburgh Labour party, asking for an assurance that the party will not cooperate with the Conservatives in Edinburgh.

The politicians – Angus Robertson MSP, Ash Regan MSP, Ben Macpherson MSP, Gordon Macdonald MSP, Deidre Brock MP, Tommy Sheppard MP and Joanna Cherry QC MP – have pointed out that the electorate “resoundingly rejected” the Tories in the election at the beginning of this month. Conservative numbers were reduced from 18 elected councillors to nine with some elected members losing what they might have regarded as safe seats.

In the letter from the SNP politicians, they explain that the reasons for that election loss are clearly due to the Conservative Party being led by “a Prime Minister who partied in No 10” while others could not meet or see their dying relatives. They also point the finger of blame at Scottish Conservative leader, Douglas Ross, who they brand as “cowardly”.

The Westminster and Holyrood representatives say the position is quite clear to anyone living in Edinburgh – that any party which works with the Tories is “giving credence and justification to its actions”.

They also state that there is a significant problem in doing any kind of deal with the Tories who do not make New Scots in Edinburgh feel welcome.

There are 63 councillors in Edinburgh and at the election the SNP improved their numbers by one to 19, Labour had much the same number at 13, Liberal Democrats doubled the number of councillors to 12 and Greens grew their representation by two to 10.

No party has a simple majority and there now appear to be two deals proposed – and which will be voted upon at the council meeting on Thursday.

The first is for the SNP and Greens to form a coalition – something backed by councillors of both groups as well as their local members.

The second option is for Labour to attempt to form a minority administration – taking the Conveners posts and looking for support from the two other opposition parties – the Liberal Democrats and the Conservatives.

Firstly they will require their help in getting the motion put to tomorrow’s meeting passed – and they could win that vote by 34 to 29 – and secondly they would need support from councillors across the chamber on any council business after that.

This to us does not mean they will need to wholly base their support on the Liberal Democrats and Conservatives moving forward – on certain items they are in agreement with the SNP and Greens – for example largely on matters of active travel there is an accord.

But quite what the terms of any informal arrangement are is unclear – and must still be approved by the Labour Party’s Scottish Executive Committee and also the Edinburgh LGC.