I had paving removed in order to make a new bed, and on digging down, I've found old paving at a depth of about 12-18 inches. Will anything grow or will I have to remove this as well?
What type of paving is it? If it's old slabs or crazy paving, I'd dig it out. Then it's done, not sure if I'd bother if it's solid concrete, that would be awful to try to dig out. Like Flower Bird says, it all depends what you want to plant there. I wouldn't try root crops if you're intending to do a veg bed, but stick to things that grow upwards, not downwards. You could try raising the level by adding compost, topsoil and manure, it will all help make your soil more productive.
We've discovered a similar situation at daughter's new, to her, garden.
Some bright spark has dumped a layer of tarmac, luckily thin & breaking up, underneath what had previously been a bed in front of where we know a greenhouse had stood.
So the job for this season/yr is to try & remove as much as possible & eventually will need a small skip- joy- as lots of other rubble/rubbish is coming to light as we explore.
Oh well, planters this yr for her veg/salad crops & hopefully by the Autumn we can have achieved some clearance. With my dodgy knee, back & arm & daughter's back this could take a long time.....
Good luck. J.