It's been a long time since I did conveyancing, but it used to be the case that searches were done pre-contract by whichever law searcher the solicitor was using.
There's two basic reasons for doing these searches:
1- To make sure there's no enforcement proceedings in train affecting the property
2- To make sure nobody is applying for or has received planning for a factory/night club/incinerator/20 story apartment building or whatever next door that would affect your decision to buy the property in the first place.
It's NOT to make sure the the conditions of planning permission have been complied with. This is achieved by a combination of the planning permission itself, architect & engineer opinions on compliance/exemption, certificates from various contractors & subcontractors, letters from the local authority etc. These should all be available pre-contract except in the case of new builds where it should be clear pre-contract what documentation re planning compliance will be handed over on closing. Planning searches will do nothing to confirm the presence or absence of any of these pieces of evidence.
If the vendor's solicitor has any sense they'll have a special condition in the contract to the effect that no questions can be asked, and none will be answered, in relation to the planning status of the property or any part thereof. This is why it's important to have all the planning issues cleared up before signing on the dotted line- if you sign and then find an issue then you have a serious problem.
To check enforcement proceedings you're still best off going through a solicitor/law searchers for this, for the simple reason that they have the experience to do it properly and the insurance to cover any errors. You don't. The solicitor should send you on a copy of the searches.
To make sure you're not going to have an open cesspit nearby (or at least not an open cesspit for which planning permission has been granted), you're probably best off checking the planning maps online. If you're buying 1 O'Connell Street, the law searcher can't be faulted for not identifying a relevant application for or grant of permission for number 5 O'Connell Street. If you're looking at a map of the same area, you can check out every application for the area, including places you'd be driving or walking through every day, to make sure you have no surprises.