I was looking at the Topping E30 DAC, which is about £140, which seems reasonable.
That’s a DAC, not a headphone amp.
You use an RCA left and right cable to a 3.5mm headphone jack.
Well, you could plug your headphones into a power outlet too, doesn’t mean you should do it.
The DAC provides line level and the whole thing will be impedance-mismatched. If you want the E30, then pair it with the L30, which is a proper headphone amp. Just be sure to get the new fixed ESD version as older models are known to blow headphones.
It’s been said that you can use these headphones with a headphone jack of your source and that is true, but I’d not recommend doing it. You’re buying mid-range headphones (let’s not count exotic cans that can cost a fortune), so get something to drive them properly. You want a good frequency response 20Hz to 20kHz, enough output power for 250Ω, good THD+N, a low noise floor and good channel balance.
Check out this video:
It’s a little older but still good. There are more reviews on that channel. There’s also a video that explains why they’re measured this way and what the measurements actually mean.
The Mackie HM-4 has been mentioned specifically above. I would not buy it for the DT 1770. The output impedance @47Ω is too high for 250Ω cans. It will work, but you will have coloration in the sound. With 250Ω you should at least go down to 31.25Ω for better performance. Maybe you can find a review somewhere with full measurements.