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You have applied for a UK Standard Visitor Visa and the processing time is taking longer than usual. You want to expedite the application because your travel plans may be disrupted.
The first step is to use the wizard at Visa Processing Times to see if your application falls within the expected times. These figures are both reported to Parliament AND audited by Chief Inspector so the public can rely on them with a high confidence.
The British Consulate General in Pakistan for example shows that most applications are resolved in 30 days and all applications are resolved within 60 days. If you are still within the expected values there's little to be done.
Some tips and techniques...
Look for emails. The status of a submitted application is not all that granular so there's not much to learn. It can be one of these...
The first and last of these are generally notified by email. Check through your email to assure any notifications have not been rerouted to a spam folder.
If the decision-maker is minded to refuse but thinks that a simple phone call to clarify a single issue can salvage the application, they will contact you. So be sure that your contact details are correct and that any incoming phone calls are recorded. They will leave a voice message with a telephone number. Otherwise note that British Consulate Generals do not engage the public and there is no way to initiate direct contact with them.
The final step is to contact the Visa Facilitation Service where you submitted the application and find out if they offer a way to "promote" your application to high priority. This opportunity is offered to end-users on a country-by-country basis. An example is the "User Pay Services" page on the VFS India site. From personal experience I can say that "promoting" an application may or may not have an effect; you cannot force them to make a decision if they are not ready to make one. For complex applications, they will take the money and continue with whatever they were doing so promoting your application may not be helpful.
About your plans...
Since the beginning of the internet the Foreign Office (in its various incarnations) has run an advisory warning applicants not to purchase tickets in advance of an application. These warnings are currently run by the VFS and the standard formulae goes...
VFS Global recommends that you do not purchase tickets or make bookings which cannot be cancelled without cost prior to the issuance of a visa, except where it is a specific requirement stated as part of the visa application.
Source: Standard VFS Disclaimer
Also, if your processing time falls outside of the published values, you can lodge a formal complaint with UKVI.
Also, the Foreign Office has a great blog entry: Top Secret ... How to get a UK Visa which may be helpful reading.