I get invites which tell me I am expected at 7 for 7.30. What time should I arrive?
'expected at X for Y' is a format sometimes used in official invitations - it's effectively a window of time where it's considered polite to arrive, without being late. In your example, 7 for 7.30, one would be expected to arrive between 7 and 7:30, with the main event (often a dinner party) taking place at 7:30 sharp.
An online example of such an invitation can be found here. Note the text in the bottom corner.
7.00 for 7.30pm
Carriages at Midnight
This is a shortening of the phrase:
Arrive at 7:00pm for a 7:30pm start.
This is often used when registration or seating etc. is required, where guests are invited to arrive at a given time, while communicating that the event or meeting is due to start later than the arrival time.
This avoids the confusion of advertising 7.00 and having people arrive at 6.30 for a 7.30 show, else advertising 7.30 assuming that people will arrive early and ready to start at 7.30 but then have guests arrive late under the presumption that 7.30 is the meeting time with a later event start.
A concrete example of this would be requesting to meet at the cinema at 7.00pm for a 7.30pm start of the show. Asking to meet earlier is to allow time for purchasing tickets and locating seats while also clearly stating the acceptable range of arrival times/consequences of being late.
For instance, arriving after 7.00pm means ticket purchase etc is rushed with limited/no time for snacks, while arriving after 7.30pm means missing the show/event (or having to order your food after everybody is beginning to eat their starter, in the case of a meal).
It also shows that arriving at 6.30pm is not required since the half-hour "overhead" has already been factored in.
Arrive at or very shortly after 7, but well before 7:30. "At 7" means exactly what it says: you are expected to be there at 7. "For 7:30" means that the main event will begin at 7:30; for a formal dinner, this would mean that the first course will be served at 7:30. The half hour in between ensures that all guests have a chance to check or put away their coats/jackets, find their places (if it's a large gathering with assigned seats), and mingle a bit.
It is most usually used in more formal invitations where there is an initial event (ie cocktails) that precedes the main event (dinner).
It is not an invitation to arrive at the later time as usually the first event is also catered for. However arriving somewhere between 7 and 7.30 would be acceptable (the closer to 7.30 the less acceptable) with arriving after 7.30 regarded as most impolite.
Another usage of this word combination ([time] for [time]) in British English is if you are describing when you're leaving for an event, and the time you intend to arrive there. For example:
"When are you going to the party?"
"I'll leave at half 6 for half seven, traffic is murder at this time of day"