How is the cooker currently wired? Is there an isolation switch, and a box on the wall behind it with a short lead running to the cooker?
Do you know what the circuit protection (MCB or fuse) is? Are we talking a stand along range with electric hob, or just an oven on a plug?
A picture of your consumer unit, the current location and where you want to move it to will probably help give better advice.
Running cabling behind cabinets is certainly possible, though the length of the new circuit may be limited by various factors, such as the rating of the cooker, the size of cable, etc. Any cabling should be properly supported though rather than just slung across the floor as often happens with kitchen fitters....
Unfortunately, there are lots of factors involved in installing a new cooker to the current regulations, which means unless you are confident in working with electrical cables it is probably better to get an electrician to look at it - cooking appliances tend to be high current drains and any issue with loose connections or incorrect wiring has the potential to cause safety problems more than some other circuits.
It may be necessary to upgrade the current protection to meet current regulations, but that will depend on your current consumer unit age and setup.
It may be worth getting a few quotes in person - the price could vary a lot depending on location but I'd have thought it should only take 1-2 hours maximum, if there is no chasing or channeling involved. Hourly rate can vary wildly depending on size of company, but I'd say the usual range is going to be 30-80. Then there would be the cable, the connection box and clips to add on top.
You should be able to get a fixed price quote from a local smaller one man band or smaller company - they are more likely to be wiling to do small jobs like this.