Convert a hardwired outlet to a plug socket

You must not "just cut off the plug and wire it in". The cable to the cooker outlet - probably 6sq mm or even 10sq mm - is expected to take a very high current and will be protected with a circuit breaker or fuse around 40A. The cable for your striplights will be designed to take about 3A. So you'll end up with a 3A cable protected with a 40A breaker. In case of a fault, your 3A cable would catch fire long before the breaker would trip. As far as replacing the cooker connection point with a 13A socket outlet is concerned; In theory, there's nothing to stop you doing this, but as the cable to the cooker connection plate will be at least 6 sq mm, you'll have a real struggle trying to get the cable to bend to your will, pushed into the screw terminals, and then getting the socket faceplate screwed into the backbox. Ideally, you'd need to sink a new backbox into the wall, connect it to the cooker connection point using 2.5 sq mm cable, fit a 13A socket outlet faceplate to the new backbox and replace the cooker circuit breaker with a 20A breaker (or 15A fuse). All wiring must be done in accordance with 17th edition wiring regs and should therefore only be performed by a registered, competent electrician.

Firstly you must apply for Part P building regulation consent to carry out DIY electrical works. The fees for this will be on your council website but are typically around £250 - £300! Once you have the consent in place you can then carry out the works, but it must be in accordance with BS7671:2008. As this is a small job, you would be better of hiring an electrician for an hour and getting it sorted.