My recommendation would be a second hand Dell Latitude. For £450 you should be able to get an i7, either with an SSD and 8-16GB RAM or upgrade yourself. Ensure you get one with a Full HD display.
These laptops are business grade - which means (a) sturdy and (b) designed so they can be repaired. Adding RAM or swopping out to a decent SSD is a case of turning the laptop upside down, removing the battery, four screws from the bottom plate at which point the bottom plate will slide off and you can swap out the RAM/SSD.
Understanding the model numbers:
Eabc0 e.g. E7440
The first 'E' means the laptop will work with a port replicator (dock)
The first number (a) is the range. '3' is entry level. '5' is mid range. '6' is higher end. '7' is higher end/ultra portable.
The third number (b) is the panel size. 2 is 12.5", 3 is 13", 4 is 14" etc.
The third number (c) is the generation. 7 is 6th gen. 5 is 5th gen. 4 is 4th gen. No, that is not a mistake.
If you search a well known auction site for 'Dell Latitude E5570 i7' (mid-range 15.6" Core i5/i7 6th Gen) you will see plenty with i7/16GB/SSD in your budget. Look for sellers with plenty of positive feedback and try and buy one in A+ condition. When you do receive the Laptop, check for dead pixels and any sign it has been dropped. I would also do a clean install of Windows 10. If the laptop was already running Windows 10, a re-install should not pose any problems in terms of licensing.
They are nice, well built machines that can take a fair amount of abuse. I've acquired upwards of half a dozen for friends and family. One needed a bit of TLC on arrival, the recipients have all been very pleased with them.