In the unlikely event you are in bed and the alarm goes off or you can hear someone downstairs, a strong lock on the bedroom door is the first thing you need. Jump up and lock the bedroom door. Burglars want to steal things, they are unlikely to try to come and find you just to hurt you, that's not what they're there for but tend to attack when confronted.
A weapon of choice, such as a torch, baseball bat etc in your bedroom is also good if you do need to defend yourself. A door jammer security door-stop or something similar will be an additional extra to prevent anyone trying to break into your room. You could also put one of these by your front door before bed if you felt it was necessary. I have a bottle of the common household product WD40 in my bedroom for "repairs" of course, but it's also very effective at stopping someone when sprayed into their eyes - this, of course, is a last resort.
Your rape alarm is a good idea, but most essential is ensuring that you have a phone with battery and signal in your bedroom that you can use to call the police as soon as possible - the sooner you call them, the sooner they'll arrive.
Keeping your door keys and car keys away from the doors/windows and out of sight will stop someone attempting to get them - some burglaries take place when the homeowner has left their keys clearly visible through a window and a passing chancer has seen them and attempted to take them in order to gain access to the house or to steal a car on the driveway.
CCTV or a ring doorbell on the outside of the door, with a sticker somewhere saying "THIS PROPERTY IS MONITORED BY CCTV" will also show any potential intruder that their every move will be caught on camera.
A home invasion is VERY unlikely and any home invaders breaking in specifically to hurt you are even less likely, however it is always smart to have a risk assessment in the chance that, if someone does break in, you'll be prepared. The best thing you can do rather than trying to confront or attack them is to put as much distance and as many obstacles between you and then as you possibly can, such as a door with a lock etc.
You said you don't have a dog, but if it's possible and practical for you to get one, they're fantastic for peace of mind. My dog doesn't bark at all during the day while we are all downstairs but once we go upstairs to bed, it's as if he feels his is "on guard". He sleeps soundly but the slightest disturbance downstairs and he goes off like a banshee. Last time it was when a bat flew into our living room window and the time before that was when one of the workers on the farm couldn't start is car so had to knock on our door at 2am! Both incidents were harmless, but I have peace of mind knowing that any intruder would be met with a loud, barking, snarling dog which would 1. alert me and 2. hopefully deter them.
Home invasions are very rare in the UK. Despite the fact that figures show they do happen, the percentage of households that have a home invasion are very, very low. 21% of burglars in the UK enter through an unlocked door, meaning that by just locking your door you're already reducing your risk greatly. Although it is a potential risk that it's safe to prepare for on the offchance it happens, please don't let yourself become too worried by this that it impacts your life. You now hopefully have some ideas to put into action that can give you peace of mind and allow you to remain feeling safe in your own home.