In case I did not spell it out sufficiently, it was no longer deemed practicable for the King (or rather Margaret) to rule from Westminster as London was too volatile and pro-Yorkist. This is a remarkable indictment of the Lancastrian government in itself. OK, it was commonplace in the middle ages for the court to go on progress, but generally they didn't go that far from the Thames Valley and they always ended up back in the environs of London.
One or two kings (Richard II springs to mind) got sufficiently cheesed off with the Londoners to punish them by temporarily moving the effective capital elsewhere (York in his case) for a time, but for a government to be effectively driven out is a horse of another colour.
For the Lancastrians the West Midlands had its attractions. They had a lot of property in the area, including a large and powerful castle at Kenilworth, and this added up to the potential of armed support. Coventry was deemed a loyal city, and councils were held there instead of at Westminster.
It was really now only a matter of time before armed hostilities broke out. On 5 November Exeter, Somerset and Shrewsbury attempted to ambush Warwick on his way to London and on 1 December, in Coventry itself, York was attacked by Somerset. Warwick and York survived but (given that the government was now in the Queen's hands) they can hardly be blamed if they felt uneasy and looked for ways to defend themselves.
There was a Great Council held at Coventry in 1457. Records of it are lost but it appears some attempt was made to pin the Herbert-Devereux disturbances on York. The peers were evidently not convinced. York was granted an annuity of £40, supposedly to recompense him for the loss of three Welsh Castles to Jasper Tudor, and his patent as Lieutenant of Ireland was renewed. In the summer he was also granted, among other things, the right to hold a market at Fotheringhay.