There are different ways you can try speeding up, or at least ease, the homebuying process, though none of these is guaranteed 

• Be proactive where you can. Whether submitting paperwork for your mortgage application, filling in forms for your conveyancing solicitor, completing ID checks, proving your funding, speaking to a broker or comparing buildings insurance quotes – get things sorted as quickly as you can.
• Consider selling before you buy (if you're already a homeowner). This may not be feasible as you'd need to find somewhere else to live temporarily. This means you will be chain-free, meaning sellers could be more likely to accept your offer, plus you wouldn't have the stress of juggling a purchase and sale simultaneously.
• Don't expect the best service if you pay for the cheapest conveyancing firm. While some delays are out of your conveyancers' hands, don't expect the best or speediest legal service if you're not willing to pay for it.

Remember,

• to ask for a dedicated conveyancer and avoid big companies that are likely to give you a new case handler for each part of the transaction
• you dont have to appoint a local Firm, as most things are completed via email/ post
• to ask friends and family, who have recently moved for recommendations. Ask your estate agent too, but remember to ask if they get a referall fee to recommend a conyeancer, as this may influence their opinion. 
• that communication is key! Check you can speak to the person dealing with your transaction and that they have the capability to take on new work.