If you plan to visit another country while you are in the UK, check before you leave your home country to see if you need a visa for that country (please check with the embassy website). It is usually easier to apply from your home country than from within the UK. This is very important if you wish to visit the USA.
If you are already in the UK, then before confirming your travel plans, it is recommended that you check the visa requirements for the country you intend to visit. You will need to do this plenty of time before you travel. For travel to Europe, most embassies describe the process as taking at least 3 weeks, but this can be longer depending on your nationality and during busy travel periods.
To find out if you need a visa for the country you are travelling to, please check the embassy website for the country you wish to visit: https://www.gov.uk/government/publications/foreign-embassies-in-the-uk
The International Student Support office has some useful advice for traveling within the Schengen area: https://www.imperial.ac.uk/students/international-students/visas-and-immigration/schengen-visas/
If you need support getting a visa, CIBT visas are a useful agency with a good website: https://cibtvisas.co.uk/