thank you for sharing your question with us.
If you have already a job offer- in Form of a written one. Then you might wanna apply for a working Visa to the UK.
In general for the UK you would need a Visa( even as tourist) to enter the country if you are not a EU Citizen.
There are different kind of working visa- depending on the type of contract you have:
Further as to the question of applying in the UK for asylum:
"Your claim might not be considered if you:
- are from an EU country
- have a connection with another country you can claim asylum in, for example if you’ve claimed asylum in an EU country before arriving in the UK"
So in your specific case I would suggest you get a working visa.
I hope we could help, if any further assistance is needed, do not hesitate to contact us.