Chain slipping on 10 speed Deore XT with new cassette, new chain and new chainrings
Are you really sure it’s not jumping to the next cog? Sounds most likely with new parts.
I’d check that:

the cassette is correctly installed and tightened (it needs 40Nm tightening torque which is a lot)
that all links of the chain move freely, especially where it’s closed (I hope you’ve used a master link or a dedicated closing pin). If you’ve used a closing pin, make sure it’s flush. If it’s a master link, make sure it’s fully closed.
that the rear derailleur or derailleur hanger is straight and not bent.

Hang the bicycle somewhere (or put it upside-down), pedal with your hands and closely observe the chain as it moves. Check that everything shifts smoothly and precisely.
If the chain is actually skipping under load it should be much worse on the smallest chainring.
Regarding:

Also, a few weeks ago, I noticed that my deraileur bolts fastening it
to the frame were very loose before this happened and I have tightened
it to ensure that it is consistent. I was amazed that everything
worked as well as it did with one of the bolts being very loose.

I assume you mean the derailleur hanger (which is usually fastened with two bolts)? It’s mainly held on by the rear wheel’s quick release axle which firmly presses it to the frame. Usually you can actually see the derailleur hanger move slightly when you tighten the quick release.

The chain was shortened to the same number of links as the last chain.
The larger of the new BBB chainrings has 2 more teeth than the
original Shimano

I hope it’s not too short now. Make sure the derailleur is not fully extended when shifting to the biggest cog while on the big chainring.