Phase One of High Speed Two - the part between Birmingham and London - is under construction. You can take a look at the route and TBM progress here:
>https://www.hs2.org.uk/in-your-area/map/

At the moment, two tunnelling machines are racing each other underneath the Chilterns (with more to launch later), prepwork to expand London Euston is ongoing, Old Oak Common station is under construction, and construction of the Colne Valley viaduct is in progress.

https://www.newcivilengineer.com/latest/hs2-timeline-of-major-events-to-2025-revealed-15-07-2022/
>HS2 Ltd has revealed the timeline for key contract awards and works up to 2025, which will see a large proportion of the construction for Phase 1 to Birmingham completed.

Per the article:
>2022
>August - Tunnelling begins on Northolt tunnel [OP: suburban London]
>September - Contract award for Phase 2a [OP: the part from Birmingham to Crewe] design and delivery partner
>October - Concept design completed for HS2 trains
>December - Invitation to tender for HS2 main works

>2023
>January - Long Itchingdon Wood tunnelling [OP: SE of Birmingham] complete, contract award for railway track
>February - Construction starts on Curzon Street [OP: Birmingham] station
>March - Tunnelling starts on Bromford tunnel [OP: just outside Birmingham]
>May - Contract award for signalling systems
>October - Contract award for Washwood Heath depot and systems control centre, all rail systems contracts awarded

>2024
>February - Tunnelling starts on Euston tunnel
>March - Tunnelling complete on Chiltern tunnel
>April - Old Oak Common west box complete
>August - Tunnelling complete on Northolt tunnel
>September - Tunnelling complete on Bromford tunnel

>2025
>May - Colne Valley Viaduct construction complete
>June - Euston tunnel complete
>September - Major Network Rail interfaces complete in Birmingham city centre

TLDR - there's a long, long way to go still, and the current work is mostly boring (pun intended) and/or invisible.