Sergeant Brunswick set off as soon as Mrs Groynes passed on told him the terrible news, that Masie had been reported missing.

The sentence is too long, therefore somewhat difficult to comprehend. Shortening it at places and adding commas help.

On his way to the town centre to meet up with Vincmeet up with Vince at the town centre, he started to play out the worst scenarios in his mind.

However, that was not to try andhe wasn't comeing up with plans to find her—he was simply too distraught to do that.

It took him a while to make outrecognize Vince in the rain.

The bad weatherrain was too heavy, he thought. It would surely hinder the search.

This sentence doesn't fit very well with the scenario.

When he finally joined Vince, he was greeted by a furious Vince thatwho blamed him for Masie’s disappearance.

Still,Yet Vince had alsostill had some information to share.

When he had last saw her, Masie was going out with a Twitt-something.

However, that was nohe did not do that to try and come up with plans to find her—he was simply too distraught to dofor that.

In this sentence "that" should not refer to an action, but rather to an object of an action. I've rephrased the sentence to refer to the scenarios Brunswick was making, rather than his activity of making them. (The correction at the end of the sentence is for stylistic purposes).

When he had last saween her, Masie was going out with a Twitt-something.