Can't turn water off

The valve where you turned off cold could be letting by, so turn off stopcock, if was stopcock, isolate out in road, then repair or even better call a plumber 👍

Seems like you're dealing with a bit of a leaky situation. Even after turning off the water mains feed, the water still coming out from under the tap is likely due to some residual water left in the pipes. Here's a quick step-by-step guide to help you address the issue: Turn Off Pump: Make sure the pump connected to the shower element is also turned off to prevent any unexpected water flow. Open Faucet: Open the faucet of the tap you're trying to change. This will help relieve any remaining pressure in the pipes and drain out the water more quickly. Drain Pipes: To fully drain the pipes, you might need to open other faucets in your house as well. This will help the water flow out completely. Collect Water: Place a bucket or a towel under the tap to catch any water that's still coming out. This will prevent water from getting everywhere and causing a mess. Disconnect Tap: Once you're sure the water flow has stopped, you can proceed to disconnect the old tap. Make sure you have the right tools for the job. Check for Seals: While you're at it, inspect the seals and gaskets to see if any of them are worn out and need replacement. This could have been a possible cause of the leak. Install New Tap: Install the new tap following the manufacturer's instructions. Make sure all the connections are properly tightened. Close Faucet: Close the faucet you opened earlier. Turn On Water Mains: Slowly turn on the water mains feed again. Check for any leaks around the new tap. If you notice any, you might need to recheck your connections and make sure everything is sealed properly. Test Pump: If the pump is part of the shower setup, test it to ensure it's functioning as expected without any leaks. Remember, if you're not comfortable with plumbing work, it might be a good idea to reach out to a professional plumber who can assist you and ensure everything is installed correctly to prevent any future leaks. I hope this helps you get your new taps installed without any further issues.

if you have pumps you have a low pressure system supplied by a tank in loft you will need to drain this.

Could just be pressure or water sat in the pipe try draining if there a drain off or opening a tap that’s at a lower point or could be from water tank in loft if you have one that would need bunging.

Sounds to me like you maybe have a gravity fed system with a cold water tank in loft and by turning the main stop cock off will only isolate mains water feed to fresh water in kitchen the tank will usually supply bathroom water if you go up in loft see if you have a large tank also you should have airing cupboard and in there will be a stop valve for cold water feed

Simple answer is if your not able isolate water at stopcock not at the meter, call the water company to fix there meter and then fix your stop tap. Once then you should be able to isolate supply for changing taps.