Would there be tides without the Moon?

Sitting at Ravenglass I got a real sense of the movement of the tides. It was New Moon so the Moon and Sun were both pulling together and there was very high spring tide. We say that the Moon causes the tides, so what would happen if the Moon was removed? There would still be tides because of the pull of the Sun. I did some calculations to work out the pull of the Sun on 1kg of water.

The size of the pull of each on 1kg of water is surprisingly low, and the Sun pulls 200x more than the Moon. But I've read that the Moon has double the tidal pull of the Sun. This is because tidal forces are due to difference of pull on either side of the Earth. I still haven't satisfied myself about how this works but with the Moon being so much closer, the width of the Earth has a significantly bigger effect.