Every time we have a shower (which is in the bath) the water leaks through the sealant around rim of bath and runs down the wall of the cloakroom downstairs. It is not a big leak but a trickle of water. Over time it has built up and caused damp on the floor in the downstairs toilet. It has now ruined 2 carpets. We have tried resealing the bath and even paid someone to do it but it still leaks.
We urgently need to replace the ruined rotten carpet but I want the problem fixed before we put down yet another floor, this time vinyl.

What can we do to fix this problem?

Thank you. Do you think we need to replace the bath with a steel one as I've read that the acrylic baths will move too much when we are standing in shower and so making leaks more likely?

I would do as Scruff suggests and look for an alternative source of water leak. I doubt you would get anything like enough water to seep through the seal around the bath to flow down the wall and soak the carpet.

I have just seen exactly the same problem at a house I've been working at. They replaced the silicon round the bath with no improvement and so I offered to have a look. I found that the bath waste had been sealed with Plumbers Mate, a type of putty, which had compressed and allowed water to run out in quantity. I would look there first.

What others have said. Essential the bath is mounted so that the gap being sealed doesn't move when you get in and out or the sealer doesn't last. Many places recommend filling the bath with water before doing the seal but it's better to ensure it doesn't move using a frame or batten as above. Perhaps use a "low modulus sealer" which has more stretch in it although I found they tend to grow mould sooner that standard products. Perhaps a small bead of low modulus injected into the gap and a standard over the top?

Instead of something like Dettol Mould & Mildew Remover which costs  costs £3.00 for 0.75L we use Tesco Everyday Value Thin Bleach which costs just 0.29p for 2L and dilute it with water. Seems to work just as well.