The following website lists UK parliamentary petitions.
You can download the data in json or csv format.

The top ten petitions over the last few years are:

​1    EU Referendum Rules triggering a 2nd EU Referendum
2    Prevent Donald Trump from making a State Visit to the United Kingdom.
3    Give the Meningitis B vaccine to ALL children, not just newborn babies.
4    Block Donald J Trump from UK entry
5    Stop all immigration and close the UK borders until ISIS is defeated.
6    Accept more asylum seekers and increase support for refugee migrants in the UK.
7    Consider a vote of No Confidence in Jeremy Hunt, Health Secretary
8    Donald Trump should make a State Visit to the United Kingdom.
9    Make the production, sale and use of cannabis legal.
10    Stop spending a fixed 0.7 per cent slice of our national wealth on Foreign Aid

Over the last year or so Brexit, the EU and a possible official visit by Trump to the UK are big issues, immigration and health are also prominent. There are some right wing petitions: 5, 8 and 10. Number 5 is calling for something like Trump's travel ban in the US. And some left wing petitions: 2, 4, 6 and 7. 

​If we take all the petition titles and remove the stop words we can generate the following word cloud:

The following post from my code blog explains how to generate word clouds.

The technical process:

1. download the manifesto pdf files
2. convert the pdf files to text files
3. use NLTK to remove stopwords and get the common words used in each manifesto

​This required two scripts, the first converted the pdf files to text files, I used the script here. The second script is on my code blog.

The results:
DUP
[('northern', 147), ('ireland', 102), ('n', 99), ('dup', 88), ('new', 40), 
('westminster', 29), ('uk', 26), ('support', 25), ('public', 25), ('national', 21), 
('people', 18), ('united', 18), ('deal', 17), ('needs', 17), ('manifesto', 16), 
('trade', 16), ('must', 14), ('also', 14), ('best', 14), ('wminster', 13), ('eu', 13), 
('across', 13), ('irelands', 13), ('economic', 13), ('identity', 13), ('military', 12), 
('would', 12), ('better', 12), ('positive', 12), ('believes', 12)]


UUP
[('northern', 51), ('ireland', 33), ('ulster', 23), ('unionist', 22), ('best', 18), 
('united', 16), ('party', 16), ('brexit', 13), ('westminster', 13), ('mps', 12), 
('local', 12), ('union', 12), ('work', 11), ('manifesto', 11), ('one', 11), ('remain', 9), 
('great', 8), ('need', 8), ('many', 8), ('yet', 8), ('would', 8), ('public', 7), 
('south', 7), ('tom', 7), ('executive', 7), ('kingdom', 7), ('people', 7), ('election', 7), 
('danny', 6), ('better', 6)]

Alliance
[('northern', 170), ('alliance', 110), ('ireland', 103), ('uk', 75), 
('support', 65), ('ensure', 51), ('would', 43), ('change', 40), ('public', 37), 
('economic', 35), ('also', 32), ('westminster', 32), ('work', 30), ('government', 30), 
('european', 29), ('direction', 27), ('need', 27), ('deal', 26), ('across', 26), 
('executive', 26), ('international', 25), ('political', 25), ('brexit', 24), 
('must', 24), ('eu', 24), ('significant', 23), 
('continue', 23), ('tax', 23), ('human', 22), ('welfare', 22)]

Sinn Fein
[('brexit', 44), ('eu', 35), ('sinn', 32), ('rights', 30), ('tory', 25), ('health', 23), 
('north', 23), ('irish', 19), ('access', 18), ('european', 17), ('vote', 16), 
('within', 16), ('party', 15), ('special', 14), ('services', 13), ('ireland', 13), 
('status', 13), ('election', 13), ('cuts', 12), ('funding', 12), ('designated', 12), 
('dup', 12), ('new', 11), ('unity', 10), ('trade', 9), ('priorities', 9), ('people', 9), 
('british', 8), ('good', 8), ('friday', 8)]


TUV
[('tuv', 97), ('northern', 95), ('ireland', 81), ('politics', 42), ('would', 41), 
('principled', 41), ('talking', 41), ('straight', 41), ('stormont', 35), ('sinn', 34), 
('fein', 30), ('people', 27), ('need', 27), ('dup', 22), ('government', 22), ('public', 20), 
('believes', 19), ('first', 19), ('uk', 19), ('must', 18), ('irish', 17), ('health', 16), 
('brexit', 15), ('eu', 15), ('one', 15), ('money', 15), ('assembly', 15), ('could', 14), 
('language', 14), ('mental', 14)]


SDLP
[('sdlp', 262), ('northern', 154), ('ireland', 104), ('new', 97), ('ensure', 85), 
('must', 58), ('support', 58), ('people', 55), ('believes', 51), ('also', 45), 
('investment', 39), ('public', 39), ('housing', 39), ('education', 39), ('better', 37), 
('government', 37), ('local', 35), ('development', 35), ('services', 32), ('strategy', 32), 
('economy', 31), ('across', 31), ('health', 30), ('areas', 30), ('community', 30), 
('sector', 29), ('economic', 28), ('work', 27), ('social', 27), ('future', 26)]
​Note the SDLP manifesto for the Westminster election can not be scanned using the pdf to text script so I scanned their Stormont manifesto from March 2017.