I was once pondering this with
@VVD0D95. We decided that Matilda would likely be a very imperious Queen, shaped more by the pomp and circumstance of the Imperial Court than her father's, and that men like Chester would likely rebel in the hope of replacing her with a puppet child King in her son Henry, but that Robert of Gloucester and Brian FitzCount would probably be great helps in holding the country together for her as long as her children are still minors.
Relations with France would likely still be fraught, but relationships with Scotland would likely be easier, given David of Scotland is Matilda's uncle. The Scots might even manage to hang on to the Honour of Lancaster for a while longer than they did OTL.
And given how fraught Matilda's relationship with the Londoners was OTL, it's possible that the de facto capital of England is moved to Winchester or Bristol, at least temporarily, even if the finance/trade stays centred around London.
Although, admittedly, my favourite POD for this is Stephen dying at the Battle of Lincoln in 1141...