My newborn (now 5 weeks old) rolls onto his side during his sleep. He always ends up with his face right up against the side of his pram and bassinet, no matter how many times I roll him onto his back, or move him away from the sides he will always end up in that position. How do I ensure he is safe, as I have noted the advice on here that head supports are not recommended?

It is not unusual for babies to wriggle, roll to side or move around their sleep environment before they are rolling.
Are you wrapping your baby?
Some babies do not respond well to wrapping & may wriggle to attempt to get out of the wrap/swaddle.
Some babies like to touch their face or suck their fingers.

You could try wrapping him with his arms out.
I think it would also be preferable to move him from bassinet to cot, as would be recommended when baby is rolling.
It is important that baby’s head & face remain uncovered & as you are doing, always place baby on the back for sleep.
Head supports & other sleep positioners are not recommended as some may create an extra risk in baby’s sleep environment.

How does he go with tummy time when awake?

Red Nose has the following information when baby starts to roll (regardless of age)

If you are using a bassinette, it is time to transfer baby into a cot as soon as they first show signs of being able to roll.
Give baby extra tummy time to play when awake and supervised as this helps baby to develop stronger neck and upper body muscles which in turn enables them to roll back over.
Make sure that baby is on a firm and well-fitting mattress that is flat (not tilted or elevated).
Make sure that baby’s face and head remains uncovered (do not use lambswool, doonas, pillows, cot bumpers or soft toys)

As babies grow and develop they become very active and learn to roll around the cot.
At this time, continue to put them on the back at the start of sleep time, but let them find their own position of comfort.
By this stage it is not necessary to wake during the night to turn baby over to the back position

Do not use any devices designed to keep baby in a particular sleep position.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over