Are you buying in topsoil because yours is very poor? More info please.

At least 3 inches for grass. Cut out a healthy section of your current grass, examine how long and deep the roots go down. Ideally, that's how deep your soil should be.

More info required, please - you could be asking how much topsoil you need to spread over solid concrete or tarmac to create a lawn or grass for all we know... if that is sort of what you're asking, it won't work, needs proper drainage, no matter how much topsoil you put on top...

Or you could be asking about adding topsoil onto an existing lawn, so clarification is essential for a good answer.

The soil should be deep enough to accommodate a deep extensive root system. There is no standard answer. Different varieties of grass grow to different depths. Alfalfa, for example, can send roots down 50 feet into the earth. Prairie grass roots can go down over 10 feet. Visit a local garden center to find out what the standard grass is for your area. I could give you an answer for Kentucky Blue Grass, but that won't help you in the UK. If you're in an area that gets a lot of rain, the grass won't have to probe as deep.