RPi Zero and USB WiFi speed

I have an OSMC install on a Pi Zero (not Zero W) with the “official” USB WiFi (bcmusb - 41…).
It is very close to an old AP that supports 11g (not 11n)

I get 1Mbps transfer rate from the Pi but much more when using iOS device (ADSL is 10Mbps and I get that on iOS).

Are there any tips / tricks to improve Zero USB WiFi speed without buying new router or USB/Ethernet dongle?

Well first I would try to figure out where the problem comes from. Use wavemon (to see connection speed, signal strength and errors) and iperf3 to test throughput against other LAN devices.

It was iperf3 that gave the the approx 1Mbps.
Will try wavemon - but my suspicion is RPi Zero USB or the wifi device driver.

dmesg might give you some clues. WiFi drivers are usually quite noisy when there are problems.