If your travel involves a connection within Europe or is on an EU-based carrier, you are protected by the robust EU261/2004 (or the UK equivalent) passenger rights. If your delay causes you to miss your connection and arrive at your final destination more than 3 hours late, the airline is legally required to rebook you on the next available flight at no extra cost. While you wait, the airline must provide "duty of care," which includes food vouchers and two phone calls/emails. If the delay requires an overnight stay, they must provide hotel accommodation and transportation to and from the airport. Furthermore, if the delay was within the airline's control (mechanical issues, crew scheduling) and not "extraordinary circumstances" (weather, strikes), you may be entitled to cash compensation ranging from €250 to €600 per person. The key is that both flights must be on the same "booking reference" (PNR); if you booked them as separate tickets, the airline is not obligated to help you or pay for a new flight.