Having flown a lot from EGHH, I would always use the ATIS as an arrival / departure aid, so I know roughly what to expect. On initial contact, just tell ATC 'G-BLAH with Information xx overhead xxx, altitude xxx on QNH xxxx, etc'. ATC then know what vintage ATIS info you're working with and will advise you if this is no longer current, etc.
AIUI, ATIS info will be updated (if needed) at 20 and 50 mins past the hour (certainly for EGHH), so you'll have some idea of when to check for updates.