Grandparents are no longer sufficient to ensure a UK passport/citizenship. The only sure way is for your mother to be a UK citizen. Father is sufficient if he was legally married to your mother at the time of your birth in a jurisdiction recognized by the UK OR if you were born before Oct 1, 1982.

Also, without residency, the EU can bar you from entering on a tourist visa if they feel you're a de facto resident avoiding the immigration process. Once barred it is very, very difficult to reenter any EU country.