Advice on job search and interviews

Recent graduate. Back home. Looking for a paralegal position in the meantime before I move to London — no specific timeline, but in maximum 6 months. My town is small and there are barely any law firms around here. I don’t have a car so cannot travel to nearby towns.

Got rejected from a conveyancing paralegal position at a top 50 law firm (the only in the area) because I said I’d like to qualify as a solicitor in the future, making them think I wouldn’t stay there for a long time (which is likely true anyway, but I needed experience).

How do I approach questions about my plans in future interviews to get some paralegal experience? Or should I instead focus on getting another position in customer service for the meantime?

Thanks!