Yes, and you've got two near-perfect matches to choose from.
Mylands Pure White No.1 is a lovely clean, crisp white, but it carries a premium price. If you want the same look for less, Dulux Snow Scene is the one to go for — it measures ΔE 0.6 from the original, which is below the threshold the eye can detect, with an LRV of 90.3. Side by side on a wall you simply wouldn't tell them apart. Crown Pure Brilliant White is just as close, also at ΔE 0.6 with an LRV of 89.3, and Crown trade tins are cheap as chips and stocked in every merchant going.
Both of these are proper bright, brilliant whites — exactly the territory Pure White No.1 sits in. They suit ceilings, trim and woodwork beautifully, and on walls they'll keep a room feeling fresh and uncomplicated.
If you'd rather a slightly softer, less stark white with a touch more warmth, COAT's Me Time is worth a look. It's a touch further off at ΔE 2.1 (still very close) and a lower LRV of 83.7, so it reads a hair less brilliant and a bit gentler on the eye. That's not a fault — some folk find a true brilliant white can feel clinical in a north-facing room. COAT also do quick-dry, low-VOC formulations which is handy if you're painting a kid's room or somewhere you can't air out for long.
The honest answer on "but is it really the same?" — at ΔE 0.6 the colour is matched to within what the eye can register. What you're paying extra for with Mylands is the depth and richness of their finish, particularly in their oil-rich emulsions. For a brilliant white though, that difference matters far less than it would on a deep, characterful colour.
Grab a sample of Dulux Snow Scene and Crown Pure Brilliant White, paint a decent patch, and pick whichever your merchant prices best. You'll have it sorted for a fraction of the cost.