I think you have some options:
Get a Windows tablet
You can keep using the tools you know if your projects are simple enough for the hardware within your budget.
Both Ableton Live and FL Studio licenses permit installing on multiple (2 for Ableton) devices, even cross-platform.
It looks like currently a £300 Lenovo Yoga 2 11.6 2.16 GHz, 4 GB RAM, 500 GB HDD convertible model with touchscreen (B00LJOTI4A) is within your budget and meets the minimum requirements for both Ableton Live and FL Studio.
Install Linux on a tablet
LinuxOnAndroid seems to exist for this purpose. If you succeed, it would be great if you could share your story at the Unix SE.
What DAW would you use though? There is a list on Linuxaudio. There is also Renoise, which has a tracker approach to DAW though. I think the one most comparable to FL Studio would be LMMS, which also runs on OS X and Windows, so you can check now whether it meets your needs. Be warned, that Windows VSTs will not run or perform very badly (with wine) on Linux (no idea about OS X VSTs).
Embrace the limitations
Try further apps for tablets:
- Audio Evolution Mobile Studio (Android), Caustic (Android, iOS) and Cubasis (iOS) might be considered compromises.
- SunVox (Android, iOS) appears to innovate for touchscreen input
In a way, compromise is unavoidable though.
Tablet apps are focused on touchscreen input and thus make compromises, compared to the precision of the mouse and the resulting permissiveness for small interface objects.
Tablets have mostly low hardware specs compared to audio workstations, which means that they can't support the processor- and memory-intensive features that a complex desktop DAW utilizes.