My 3 month old has become very physically active in his sleep at night, which generally does not seem to phase his sleep, but because he is getting much stronger his body moves around a lot and I can notice. We used to use a Muslim wrap to tuck him in to end of his bassinet (like a little tuck in sheet) but through movement, he keeps kicking this off. He’s in an appropriate sleep suit for age and temperature (hasn’t started to roll over yet). Should we remove the Muslim wrap at the end of bed as make shift tuck in sheet and just let him sleep in his sleep suit (love to dream).

Many babies will wriggle/squirm & move in their bassinet/cot - he may be attempting to roll.
Once baby is showing signs of rolling they need to be transferred to their cot & cease swaddling (including swaddle suits eg love to dream) - babies need arms free & the space of a cot to roll well.
Most babies show signs of rolling around 3 months of age ie attempting to roll.

Red Nose recommendations are to “always place baby on back for sleep” not baby must always sleep on their back.
https://rednose.org.au/article/red-nose-safe-sleeping-recommendations

Most babies will be rolling over by 4- 5 months. Some earlier, some later.
This is very normal as babies grow & become stronger.
Many babies then prefer to sleep on their side or tummy.
This is not something that needs to be stopped. It is important to make the “new” environment as safe as possible.
https://rednose.org.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over 

Ensure mattress is firm & flat & nothing soft or loose in his cot.
Continue to always place your baby on back for sleep.
Cease using a muslin wrap (or any other product) to restrain or stop him moving in the cot.

How does he go with tummy time when awake?
Increasing tummy time when awake is important to build upper body strength to roll well (both ways)
This might mean increasing frequency of tummy time, rather than how long he is on his tummy each time.