Hello Ruth - welcome to Rootschat.
The Two Brewers was in West Mills, opposite the Town Mill. It was owned by the West Mills Brewery (over time Slocock's, Hawkins & Canning, T E Hawkins, Hawkins & Parfitt's South Berks Brewery, H & G Simonds). The earliest record I have is from 1761.
Sadly the pictures on newbury.net that I and Brewmaster referenced earlier in this thread are no longer available.
http://www.francisfrith.com/newbury,berkshire/photos/the-church-from-west-mills-c1955_N61020/ shows the Two Brewers on the right. I suspect their dating of 1955 is a little early as there is no sign of the Two Brewers' inn sign that hung on the pub until it closed in late 1955.
The Two Brewers went at a time of pub rationalisation; Reading brewers H & G Simonds had bought three of the four Newbury breweries to survive WWI and hence owned almost all the pubs in town. Some of these were still running under beerhouse licences. The licensing magistrates were loath to convert beerhouse licences to full licences so Simonds did a deal whereby they closed four fully licensed houses and transferred the full licenses to four beerhouses which they felt had a better future. So the Two Brewers went and the Castle in Northbrook St got a full licence. Ironically it was only a few years later that all surviving beerhouses were granted full licences as the magistrates had had a change of heart and no longer worried about maintaining the old restrictions.
Thanks for giving the relationship between Dew and New - I suspected something of the kind after finding a description of Dew's funeral a couple of weeks ago (see image).