NGO stands for Non-Governmental Organisation; this includes both charities which are registered as such in the UK and other not-for-profit organisations which are not charities, normally because they are not eligible for registration (for example because they politically campaign). International charities are much more likely to refer to themselves as NGOs.
There are 160,000 charities registered in the UK with a total annual income of £51 billion. Tens of thousands of these are small, often local, charities with no employees. At the other end of the spectrum are around 1500 charities with a turnover of over £5million and most job opportunities are likely to be with these.
There are several broad categories of charities in the UK: medical care/research and disability (contains many of the biggest); environmental/animal welfare; children; older people; international development. You will almost certainly take a large pay cut if you choose to move to this sector so you should think hard about what kind of charitable cause motivates you most to make this worthwhile (plus you'll get grilled on this in an interview). There is a lot more information on the Charity Commission website and on individual charity's websites too.
Some of the biggest charities do have legal teams which will normally have a general in-house role and, if big enough, a small number of specialist lawyers e.g. intellectual property for a medical research charity or real estate for a charity with a lot of shops. In addition, there are a very small number of human rights/legal campaigning jobs (e.g. at Amnesty International) but these are extremely competitive and generally require higher degrees in international law.
There are lots of different types of job in a charity which a former lawyer may be able to do depending on their skill set and their pre-law qualifications including: policy/research; technical advice (e.g. science or education); media and communications; project management; or fundraising. However, every one of these jobs will be extremely competitive (particularly for international charities) with many applicants having considerable experience in the sector. It can, therefore, be sensible to apply for in-house legal/compliance/risk job and, once you're working there, gain experience with other teams. The in-house jobs will still be extremely fulfilling as you will be helping the beneficiaries of the charity and learning more about the sector.
The atmosphere is totally different from a law firm; everyone is there because they believe in the cause. It's not full of professionals but different types of people on different career paths and no-one is motivated by money. A private practice lawyer will more than likely take a significant pay cut - most 'starter' type jobs in a charity will pay between £20k to £35k. The working hours will probably much shorter than you're used to (around 35-45 hours a week depending on the role) but you will still be expected to work hard as each job is so sought after.
Although it is competitive, many charities value the commercial and corporate experience that a former lawyer can bring. If you don't want an in-house job (which can be sensible, see above) then you will need to show that you have the necessary skills to do the job which might not be obvious from your legal qualification (e.g. project management or communication) and the passion for the cause. It will most definitely help your application if you have undertaken voluntary work before applying - it doesn't necessarily have to be in the same field as the charity (although it would help) but could be with a local organisation or through your firm's pro bono scheme. If you have any annual or unpaid leave available you could volunteer in the legal team of a very large charity (like Save the Children) to see if you like it and put on your CV.