Most other products that you hold are totally separate, so moving your current account won't affect the others and it's fine to do. In fact, even if you have a direct debit set up to pay them, that'll automatically be moved to your new bank account for you, so this shouldn't put you off switching.
There are a few special regular savings accounts that are linked to current accounts (where you get a special rate if you've got the current account) that you could lose if you move bank. If you have one of these, check whether the new bank offers something similar or perhaps even better.