Floorstanders might not be the best option in a smallish room.
I'd recommend looking second hand to maximise your available budget.
Speakers I'd be looking at b&w, you might get the older 6 series or cm series for your budget.
Kef although you maybe looking at the Q range, the R series is much nicer.
You might be able to find some oldish pmc's which will be superb.
If you have some pennies left for an amp then something from the Arcam diva series is certainly worth a look. Also rotel did some nice amps a few years back. Rega is pretty good and has a similar sound to Naim.
I think we need to focus on what you mean by Upgrade?
Does that mean an addition to the existing system?
Does that mean an improvement to or replacement of existing components?
And what do you want to accomplish? If you simply want speakers with a bit more impact, then Floorstanding in proportion to the size of your room would be a good place to start.
Are the specific features you would like that you don't have now? DAC to allow you to connect the TV to the Stereo for movie watching? Network Streaming of Audio content? Access to Internet Radio? Perhaps a wireless connect between the Mac and the amp?
The Cambridge 350A is a pretty basic amp. Not high power, but should have sufficient power for all but the exotic speakers. That said, more power is always a good thing. Though I'm not so sure that is your priority right now.
You can't get what you want until you know what you want. I'm not necessarily speaking of specific equipment but more conceptually. What is the goal you wish to achieve, then we can focus on what equipment will achieve that goal.
Can you give us the dimensions of the room?
Can you tell us how you use the system? Music only? Movies only? Music and movies?
What type of music do you listen to? Jazz? Rock? Pop? Etc...?
What are you goals? More clarity? More impact? More bass?
Next, though a bit personal, tell us something about yourself? Why a system in a bedroom? Are you a student living at home? A student living in Student Housing? A working person who has a second system in the bedroom? Is this a bedroom used as a bedroom, or is it a bedroom used as a Study, Library, Man Cave, etc....? Again, these details will help us zero in on the specific equipment that would suit your circumstances.
At £700, you could almost start with a whole new system. Though it might take you a bit over budget, you could sell your existing system, and make up that difference.
Minus whatever you can get for your existing system. The Cambridge 651A with USB-PC would allow you to plug your PC directly into the amp for the best performance.
The above is just an example, there are other amps with other features, and other similarly priced speakers.
For example, theYamaha RN500 Network Receiver has AM/FM, DAC -2xOptical, 2xCoaxial, 2xUSB-media, Network Streaming, Internet Radio, and 80w/ch, priced at £450.
That would strain your budget, but nice amp, nice price, lots of features, and if you sold the old system, you could probably get some nice speakers to go with it. With a £700 budget and the Yamaha RN500, you would have £250 left over, so you would need to raise another £200 to have a high enough budget to get the Diamond 155 speakers. I suspect you could easily get £200 or a bit more for your old system.
If you want to keep your current amp, and come up with a reasonable upgrade, though again I don't know your specific needs, you could get a DAC (Cambridge DACMagic 100 = £150), then add some really nice speaker which would be in the range of £500/pr. That takes you right to your budget.
But, not knowing what you want to achieve, I am somewhat shooting in the dark.
By best guess is to unload the existing amp and speakers, and start again. You can get a better amp with more power and more features, and better speakers as well and stay very close to your budget.
Which amp and which speakers, depend on the room size and how you use the equipment.