Wiring undershelf strips into lighting circuit

I am fitting some (Ikea) fluorescent under-shelf lighting. It's a 'modular' design, allowing several strips to be linked together, then plugged into the ring main (3amp fuse in the plug).

However, I want to wire the strips into the lighting circuit, so is ok to simply remove the plug and wire in? The only problem I can see is that the lighting circuit is protected by a 5amp fuse, whereas these strips currently have a 3amp fuse in the plug. Would I have to insert some kind of inline fuse? Or is the difference unimportant? Also, there is no earth wire in the strip cable, so I guess I just don't use the earth wire in the lighting circuit.

Hope my questions make sense, and thanks in advance for any advice.

can you spur off the sockets in to a switched FCU (with 3amp fuse) and take the lights from the switched side of the FCU? This will also enable you to switch them seperately rather that them coming on with the main light

Thanks for your suggestion: I guess in theory I could do that, however I actually want to have all the lighting controlled by the lighting switches. Sorry I didn't explain the setup clearly:

There were originally two lights at each end of the room, controlled by two light switches. One of these switches now controls the halogen downlighters, and I want the other to operate the under-shelf lighting, hence the desire to wire the strips into this circuit. Is there any objection to doing as I suggest, except for losing the 3amp fuse?

Yes you should be ok with that, Do you know the size of the cable your putting in? might be an idea to put a wee 3 amp FCU in-line, above the units out the road, just to be sure, an unswitched one will be fine, Unless ofcourse the cable is sufficient for a 5A load which I imagine it would be but if your unsure i'd go with the above, hope this helps a wee bit

The only thing with cutting the plug off and wiring it in will make the work notifiable to LABC under part p of the building regs (England + Wales).