When identifying a conifer it is always useful to look at the cones. Do you have any photos of cones?
Superficially it looks like a species/cultivar of Cupressus.
Where is it growing?
Is it wild or cultivated?
The tree is growing in my mum's garden in the North of Scotland. She rescued it as a tiny almost dead plant many years ago from a garden centre and nobody has ever been able to identify it. Not sure about the cones, will have a proper look next time - my daughter took the photographs. Thank you for your interest!
From a garden centre - OK - that broadens the possibilities.
We'll see how we get on, as & when you can post further photos, such as cones. Once I've seen the cones, I may have other questions. There's a good chance we can get a reasonable ID (genus), and a fair chance we can get to a shortlist of possible species.
It is probably a Cupressus or Chamaecyparis or Thuja, or maybe another related genus I can't bring to mind just now.
If so, the cones will be round and lumpy (smooth when new, cracked open when old), down to the size of your little finger nail - so you might not have spotted them under the tree because of their small size and not looking quite as cone shaped as one might expect.
By way of example, this link shows the flowers (as in your latest photo) and conces - http://lh2treeid.blogspot.com/search/label/Cupressaceae
But if there are no cones at all, it could be a hybrid (especially if from a garden centre).
The obvious candidate is Leyland cypress (X Cupressocyparis leylandii), but that produces very little flower; your photo shows otherwise
I'll leave you to do some looking, armed with that extra info.
Bear in mind, that horticulutral forms (cultivars) of the species you may come across can look rather different (height, colour, habit, etc.) from the true species (which you may find in your searches).
If you find some good candidates, please post here.
If not, don't be surprised - there are thousands of conifer cultivars out there.
I shall scratch my head some more also.
But we may need to wait until later in the year, to see if little round lumpy cones form. Then we can look at those to narrow down the search.