It's perfectly legal. Simply looking at something (with or without visual aids) in a public place is (as far as I can see) never illegal. Even if you were watching a top secret military installation from a public place, there's no specific offence. (However, if you made any notes as to what you'd seen, you would have been contravening the Official Secrets Act).
In general, you're not only free to view things from a public place, you can also photograph them (with both still and moving images). There are specific exceptions relating to such varied things as 'official secrets' and 'voyeurism' but it's not an offence to photograph someone, or to watch them with binoculars, from a public place - even if they're in their garden or inside their house.
Actually, if you look 'official' (e.g. by wearing a high-vis jacket) the police seem to assume that you must be 'legitimate'. With a colleague, I spent 3 days carrying out a survey of pedestrians and cyclists on a cycle path in Kings Lynn. We were positioned right by the gates of a secondary school. Even though our instructions told us not to interview anyone under-16, we still asked loads of 6th formers about their journeys. I was expecting a visit from 'Old Bill' very quickly but it was well into the 3rd day before a bored PCSO (who'd previously walked past us many times) bothered to ask us what we were doing!
Chris