Is there any way to access English court records and adoption records for the 1880s ?
OLIVE TREE ANSWER: Dear Diane - Unfortunately you haven't given me enough details to hone in on a specific answer to your question. Details would be location, location, location! English records are sometimes kept country-wide, other times they are county specific, town specific or even parish specific.
You've also not told me what kind of court records you want (other than adoption)
So, since I don't know where in England you are looking, here's the best advice I can give you. First, go to FamilySearch catalogue and search for court/adoption records in the locatio of interest to you. You will see immediately what, if anything, is available on microfilm or in book form.
Next, go to the National Archives UK tutorials on Olive Tree Genealogy Blog. If you have not explored the Archives you are in for a treat! You can search their catalogue to see what is available in English records or use the tutorials on Olive Tree Genealogy to search for a specific ancestor.