You're going to have a lot more problems than connectors.
£400 isn't enough to buy a kit and a battery that can supply 1000w. The cheap 48v batteries can't provide enough current. Expect to pay around £350 for the battery alone. You'll have to pay around £50 duty, etc, if you buy one from China. If you're looking at ebay, type 48v 1000w battery into the search, not just 48v.
You will also need to factor in decent hydraulic disc brakes, which means rotors as well as calipers and levers. When you're travelling at 30 mph with a 1000w kit on your bike, it takes 5 times as much energy to stop your bike compared with travelling at 15 mph on a normal bike. Pedal your bike at 15 mph, then see how much effort it takes to stop quickly, then multiply that by 5 to get an idea of what's involved.
Have you include the price of two torque arms, which will also be necessary?
To answer your question, you will always need to change/add connectors to your battery unless you buy the whole kit, including the battery, from the same supplier and you confirm with them that they have matching connectors, which they often don't.
Is it time for a new plan? Sorry if I spoilt your dream, but life isn't always simple.