Unplayable Lag Despite Fast Internet


While trying to play on my home WIFI network, 95% of the time I got a terrible lag lasting several seconds for every thing I do in any battle (Practice and Solo play) making it unplayable due to its multiplication.

The game works well on all other and even significantly slower networks, which makes me totally confused about what could I do with it.

Windows 10. Surface Pro 4 (4GB RAM)
25/5 Mbsp and 29ms latency on www.speedof.me

I’m using the native client, but the web client has the same problem.
Guess Steam has no chance of making it any better?