My baby is 7 weeks old and has started wriggling so much in his sleep that no matter how tightly I tuck the blankets he kicks them off. I am now putting him to sleep with no blankets in fear of him kicking them into his face. He now manages to wriggle his way to be squished sideways at the bottom of the bassinet. Is there a way I can stop this safely?

There is no need to stop your baby from wriggling & changing his position, but it is important to make his environment safe in light of what he is doing.
Many babies will wriggle & change position (like you describe) at a young age. Removing his blankets has reduced the risk of his head & face being covered.

Often this can mean that baby is soon going to be rolling.
Are you still wrapping/swaddling him?
Some babies just do not respond well to wrapping & like their arms free.
Often these babies like their arms free or like to touch their face or suck fingers & will wriggle to get free.
How does he go with tummy time?

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 tummy.
*It is important that you move him from bassinet to his cot & cease wrapping once he is rolling or attempting to roll.
*Baby needs arms free & the space of the cot to roll safely.
I would suggest that you cease wrapping & move your baby to his cot, rather than a bassinet.

Once he is rolling it is important to make the environment as safe as possible for this to occur.
Continue to place baby on the back to sleep.
Ensure cot mattress is firm, well-fitting & flat.
Ensure there is nothing loose or soft in the cot.
Preferable to use a sleeping bag when rolling that has appropriate size neck & arm holes.

Red Nose has the following information when baby is rolling.
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.com.au/article/what-do-we-do-now-that-a-baby-has-started-to-roll-over