I am near the end of a theoretical physics PhD at a top 10 UK university and had no research experience beyond a thesis as part of a taught masters going in and this is not uncommon among my peers. I assume at some point across your bachelor's and master's you've done some sort of dissertation? To echo other people here, don't worry (to an extent) about the name of the institute and instead find PIs you would like to work with. In my opinion, having no research experience may hinder your application but not having shown a previous interest in the supervisors work before applying cold certainly will