Do I need fire doors?

If your doing it on a single AST I don't think there is a legal requirement too, BUT for the sake of a few hundred quid, it will make you sleep better at night, I always keep in mind, even if something is not a requirement, when it comes to safety, if the worse happens, you will be stood in the dock and asked for the reason why you didn't fit them!

If you need to replace the doors or doing a major redecoration anyway, why not?

There may be certain rules set by your council about fire doors and other fire protection measures if you are intending to let the house as a houseshare/HMO (more than five tenants and more than two storeys). I'd check with your local council about licensing requirements for houseshares.

Fire doors, especially if they have intumescent strips and self-closers, can change the feel of the house and make it feel more like an institution. Students quickly tire of the sound they make and the constant banging of doors when the self-closers are set poorly, so they prop self-closing doors open with fire extinguishers and the like, rather defeating the point of the exercise. Illuminated fire signs also to my mind make a house feel like a set of bedsits or a hotel, so I would avoid these if they are not a requirement.

Fitting inter-linked smoke and radiant flame alarms (in the kitchen) is not a cheap job, when you factor in the disruption to tenants and all the redecoration, and it can lead to endless hassles because modern sensors are so sensitive and will go off at the slightest whiff of burnt toast. This leads the tenants to turning off the smoke alarm circuit at the mains and removing the backup batteries from the sensors, which again rather defeats the point of the exercise.

It's worth speaking to your council as we certainly found ours very helpful (only needed fire doors from open plan lounge/ dining kitchen to hall and from open plan room to downstairs bedroom). Modern fire doors look like ordinary doors, but Tony Atkins is right that students tend to prop doors open. This not only stops them working but also damages the closing mechanism so that it keeps needing to be adjusted.
If you can afford it, interlinked smoke and heat alarms are a good idea and the regulations on these even for normal residential properties are becoming stricter all the time. Again your council will advise you.

Get some prices for fire doors, why not? I had 7 fitted and decorated for £500. Not too bad I thought. Coincidental a few months later my local authority announced they wanted to bring in additional licensing so it was money I will be forced to spend anyway.

Your local authority could do the same and we all know government moves our goal posts all the time.

As well as interlinked alarms, consider fire extinguishers and on every floor and fire blankets and extinguishers in every kitchen.

Better safe than sorry.