Short answer: yes, you very likely qualify — and at a rateable value of £13,500, the relief is generous.
How Small Business Rate Relief works
Small Business Rate Relief applies in England to properties with a rateable value below £15,000. If the rateable value is £12,000 or less, you pay no business rates at all; between £12,001 and £15,000 the relief tapers on a sliding scale. GOV.UK's own example uses almost exactly your figures: a rateable value of £13,500 gives 50% off your bill. So you'd expect roughly half the standard rates bill — well worth having.
Conditions to watch
The main condition is that it's your only property — which it is. If you later take on a second property, you can generally keep the relief as long as each additional property has a rateable value of no more than £2,899 and the combined rateable value of all your properties stays below £28,000 in London (£20,000 elsewhere). Since this is your only premises, you're comfortably inside the rules.
It's not automatic — apply to your council
The relief isn't applied automatically. You need to contact Hackney Council, which administers business rates for the area, and apply — if you don't ask, you don't get it. You'll need your rates bill reference and the property details. Check your bill against the current rating list: relief is calculated on the rateable value in force, so make sure the £13,500 figure is from the current list. Apply promptly, because relief is usually only backdated so far.
One more thing to check while you're at it: as a new shop, ask the council whether any other local reliefs apply to you — but Small Business Rate Relief is the main one, and at 50% off it makes a real difference to your overheads.
Bottom line
- £13,500 rateable value → qualifies, roughly 50% off your rates bill.
- Only property → inside the single-property condition.
- Apply to Hackney Council — the relief is not automatic.