Company's gone bust, is it worth pursuing the new one?

It would depend on if they have defaulted on any debts or behaved dishonestly in any way. For example, did they build up their debts only to sell all their assets for less than their true value and then gift or sell them to the new one. If any of the directors have a negligence claim to answer to then they might also be liable for that reason. If they have closed and started again with a new company, that in itself is perfectly acceptable. If they have intentionally avoided liabilities through the closure of the first business and opening of the second, then you have good chance at it. The best way to deal with this would be to call them and ask if they are willing continue your contract and custom through the new company. If they aren’t, give up or be prepared to do a substantial amount of research. Most business people aren’t out to rip off customers, even the ones that have failed and started again. “Failure is not falling down but refusing to get up.”