First, I would make sure that the tree isn't planted too deep. If there is a definite soil line from the field it was grown in, make sure that that is still visible, though not more than a cm or two higher than the present soil level. Without a definite soil line, keep the topmost root no more than a cm underground.
The next consideration is watering. I would give it at least 20 liters per watering, about every 2-3 days, in your climate. A dose of seaweed extract will also help it to form roots. 5-8 cm of a coarse compost will help it to stay moist between waterings.
I wouldn't worry too much yet, because Silk Tree is often a late sprouter. Ours sprouted about a month ago, but most other deciduous trees here sprout about a month earlier than that.

I'd emphasise watering - you don't say where you are in the UK, but if its anywhere in the South, it's been as dry as the Sahara for weeks now. New trees need 2 gallons of water a week for their first 2 years, which you will have to provide during dry spells. Leave the hose on a slow trickle at the base of the tree for at least an hour to provide immediate help if you've not been watering sufficiently - or at all.

Bamboo would know better about the watering than I do--I garden in the Arizona desert, so I always over estimate! Still, it's difficult to overwater a Silk Tree. They must be a riverside tree in Iran.

Tug, I note you've said 20 litres - I have to confess that I have not a clue as to how that relates with my 2 gallons, its beyond my arithmetical capacity (not being my strong point, math...) so for all I know you've recommended twice as much as me, or half the amount, lol!

20 liters is a little more than 5 gallons, about what we usually water a new tree each time, here in the desert--but we usually water every day for the first couple of weeks.