There are a number of water fountains throughout the terminal –

At the Assistance Area before you go through security and also beyond security:

Within the main departure lounge, behind Bottega Prosecco Bar & Cafe

Within the main departure lounge, adjacent to the toilets behind Number 1 Lounge

International Pier by the departure gates

Pier Bussing lounge

North Baggage Reclaim area – Arrivals

Alternatively you can request tap water at any food/catering outlets.

From the Airport twitter feed

#plasticfree @bhx_official

There is one in the main departure lounge behind Bottega Prosecco Bar. There are another two next to the toilets behind the Number 1 airport lounge. There are a further four on the International Pier, next to each of the toilet blocks, and there is a fountain in the Pier Bussing lounge.