Yes, definitely.
The word "tracker" is misleading - it's not tracking your location, it's keeping a record of your Bluetooth pinging off other devices.
Without the ability to do this sort of tracking, we're destined for lockdown until a vaccine or costing thousands of lives. How come people are so comfortable having their lives dictated by the lockdown rules, but the idea of this is preposterous?
Having real-time data on people testing positive and how many people they are "connected" to will also be hugely beneficial in order to learn more about the behavior of this virus and be able to model it more accurately. Currently the best scientists can do is very crude modeling because there just isn't the data available to fit anything more sophisticated. This would totally change if there was a picture building of how it actually spreads. People are keen to follow "the science", while simultaneously tying the scientists' hands behind their backs.
How many of you who say "definitely not" to this also merrily click "agree" to the terms and conditions when downloading other apps? Your average app stores as much data as it can get away with yet this most don't even consider it.
However, I do hope that they make the code open-source. I trust the UK's techies to bug-check and look for unexpected code far more than I'd trust the government's assurances that this is safe.
Finally, we are genuinely being monitored pretty much all the time. Any time you drive your car. Any time you use a bank card. Your computer watches your internet browsing and stores SO much data. I really do fail to see why people are suddenly drawing the line at contact tracing.