annie46: Are there any other steps I can take?
Firstly, your savings are irrelevent. Given a good credit history, and I'll come back to that, the amount of credit granted will be an "affordabilty" assessment mainly based on the income and outgoings declared in the application but also the issuers policy.
Did you try negotiating a lower figure with Egg, say £5000?
If you are travelling you would be better off with another card anyway. My suggestion is to apply elsewhere. The limit granted will be a better indication of affordabilty in a card issuers eyes. Avoid a 0% balance transfer card as they have stricter eligibilty criterion.
But before you go further, if you have not already done so recently I would strongly recommend you check your credit report from either Experian or Equifax to ensure it is complete and accurate and doesn't list unused available credit that you are unaware of.