No. PC World, for instance will reduce the price of the PC by about £100-£150 accordingly.
But modern monitors are bigger and better than old ones angie ! Also they are very much cheaper than they used to be. I take it that you are using a modern flat-screen monitor ? I use a 23 inch TV from Tesco as my monitor and I can use it as a TV and/or DVD player, as well as with my PC. The size is very useful and an even bigger one would have been even better !
If the monitor isn't actually part of the computer itself, and only attached to it by a cable, then you can keep it and re-use it.
However, you may wish to consider buying a laptop - you can use your existing screen (& probably keyboard) at the desk, with the advantage of being able to use the laptop in other rooms if you want. Another advantage is using the laptop screen and your existing screen to view (for instance) TV on one and the internet on the other.