I got sent funds but I do not have enough space on my computer to update bitcoin core and therefore the funds will not come is there anyway to cancel the transaction. The website I got the funds from said they cannot cancel so can I cancel.
It is difficult to cancel a Bitcoin transaction after it's been sent, and it cannot be done by the recipient, only by the sender. If the transaction has been confirmed, cancellation becomes impossible.
However, the funds are not lost. They will be waiting in the address until you claim them. You can either eventually finish installing and syncing Bitcoin Core (possibly on another computer), or you can import your wallet.dat file into some other software with lower resource requirements, and you will be able to spend your funds then.
If you lack free space enable disk space restrictions via settings menu > options > main tab. You will still need to download the blockchain but it'll automatically delete blocks that it has verified to lower disk space usage. The lowest you can set the amount there is 550 megabytes. However if you do that it'll use about 3.5GB so that's the minimum amount of free space you need.
Bitcoin core doesn't have to be running for you to receive bitcoin so don't worry if the above takes a while. You haven't lost anything and will get to spend your coins once the client is synced.