Hotel told me that there is no overnight luggage storage. Are luggage storage facilities safe? Will need 2 day storage for Kings Cross and 2 day storage for Paddington. Other option is to bring luggage to Edinburgh and Bath.
You will find plenty of options in and around both stations. Many are well known companies. Can't say I have heard anyone reporting any safety issues at any.
The UK does not really offer traditional locker storage like other European countries, at least not in train stations.
You can find luggage storage services inside Kings Cross Station and Paddington Station and other major London stations. The company is called Excess Baggage. It's not available 24 hours, but they do provide overnight storage. Be aware, it's pretty expensive. You can book online or pay in the station.
Per bag
0 - 3 hours = £7.50
3 - 24 hours = £15
24 - 48 Hours = £22.50
48 - 72 Hours = £30
There are alternatives to Train Station luggage storage services. For example, CitySpareSpace partners with independent businesses that provide luggage storage. They have storage locations all over London (Kings Cross, Waterloo, Paddington, etc.) and the UK. They're more affordable, and some locations are open 24 hours, one near near Kings Cross. Their partners have security cameras, security tags for the bag, and a reimbursement guarantee. An online booking is required though, as their partners don't accept payment in the shop.
Per bag
£7 per bag (per day)