Hello, wanted to check on connections at LHR T5. I am flying from Seattle to London and then onward to Budapest. I have an Indian passport so have all the required visas. I have tickets on separate reservations. Contacted BA and they said that WOULD NOT check my bags thru even though I am BA lifetime Gold. So decided to travel handbag only as no interest in waiting for 3 hours in T5 immigration lines to check back in. Question is, can I connect through airside to my flight to Budapest with my online boarding pass or would i need to go to flight connections helpdesk? Not done this before so guidance will be helpful.