First of all, do not simply ignore the first coupon and walk up to the counter in EWR expecting to check in for your flight to Gatwick. Your reservation will already have been cancelled. The airlines are not required to accept ticket coupons out of order, and ordinarily will not do so.

The good news, is that, contrary to one of the posts above, your remaining itinerary is a perfectly good open jaw. In fact, buying a ticket EWR-LGW-SFO as an open jaw (or award ticket), with or without a connection in EWR on the return, would not be a problem. The catch is that, since you are changing your routing, they might insist on re-pricing the ticket at today's price. A better result would be if they just re-issued the ticket showing the new routing, based on availability in the originally ticketed fare class, plus, probably, a change fee. If the agent's attitude suggests you're going to have a problem, I recommend you take that important call that just came in on call waiting or your cell phone and start again later with a different agent.

Reason open jaw is ok:
Distance SFO-EWR is shorter than either EWR-LGW or LGW-SFO.