Hi, and welcome to FlyerTalk.
I'll move this to a more useful forum for replies.
That being said, 2.5 hours is quite marginal, IMO; 3 hours is a more reasonable minimum connection time.
Your options include an expensive taxi, a less expensive (but not cheap) "Mimi" cab arranged in advance, the National Express busses. There is no direct rail link.
https://www.londontoolkit.com/travel...s_transfer.htm
http://www.nationalexpress.com/airpo...ick-coach.aspx where you can see schedules, etc.
http://www.travelstart.co.za/blog/ge...hrow-airports/ which says
Heathrow to Gatwick by Bus
The bus is the most direct way of connecting between the two airports. There’s the National Express Bus which is the only direct connection, it leaves up to 6 times an hour and takes about 1 hour and 15 minutes to make the journey – it can take longer at busy times. It will cost you £19.50 per person each way. Tickets can be bought online, from the ticket desk at the airport or from the bus driver and the bus can be boarded at the bus stations at terminal 5, terminal 4 or the central bus station serving terminals 1 – 3.
But, please tell us more detail; the more explicit information, the more we can possibly provide some guidance. E.g. is this on one ticket, one airline or alliance? Etc.
JDiver
Senior Moderator