The trade you have outlined here is basically short EUR/GBP. You are better off trading that pair directly and not by doing the seperate trades as you will have two spreads going against you and the seperate carries will also be negatively skewed against you too.
Keep in mind that forex trading is effectively spread trading already. When you trade GBP/USD your making a spread trade on the relative values of those two currencies. You don’t spread trade pairs against each other because if you think GBP/USD is going to rise faster than EUR/USD (or fall less quickly) then that means you think GBP will be stronger than EUR. That’s a falling EUR/GBP rate.