Low cost webhosting with transfer help needed

Looking for a low cost webhosting provider who can transfer webhosting from the current webhosting company to their webhosting account. The old account has a large number of addon domains, most of these domains have expired, only three blogs have to be migrated to the new webhosting account.
However mySQL tables for these webhosting account are rather large at 51 MB and 6 MB so looking for a competent hosting provider to transfer the database without any problem.